Math / Algebra

QuestionExplain the process of finding the $x$ -intercept of a linear equation.
Describe how you would graph a linear function using its intercepts.
Why is it useful to know the intercepts of a linear function?

Studdy Solution

STEP 1

What is this asking? We need to explain how to find the x-intercept of a line, how to graph a line using its intercepts, and why knowing the intercepts is helpful! Watch out! Don't mix up the x-intercept and the y-intercept!

STEP 2

1. Find the x-intercept
2. Graph using intercepts
3. Why intercepts are useful

STEP 3

To **find the x-intercept** of a linear equation, we need to figure out where the line crosses the x-axis.
Remember, the x-axis is where the y-value is zero!

STEP 4

So, we set $\ y = 0$ in our linear equation.
Let's say our equation is $y = 2x + 4$ .
Substituting $\ y = 0$ , we get $0 = 2x + 4$ .

STEP 5

Now, we solve for $\ x$ .
Subtracting 4 from both sides gives us $-4 = 2x$ .
Then, dividing both sides by 2 gives us $x = -2$ .

STEP 6

So, our x-intercept is $\ (-2, 0)$ .
Remember, it's a point, an address on the graph, not just a number!

STEP 7

To graph a line using its intercepts, we need both the x-intercept and the y-intercept.
We already know how to find the x-intercept.
The y-intercept is where the line crosses the y-axis, so $\ x = 0$ .

STEP 8

Let's use our example equation, $y = 2x + 4$ . Set $\ x = 0$ to get $y = 2 \cdot 0 + 4$ , which simplifies to $y = 4$ .
So, our y-intercept is $\ (0, 4)$ .

STEP 9

Now, we have two points: the x-intercept $\ (-2, 0)$ and the y-intercept $\ (0, 4)$ . Plot these two points on a graph.

STEP 10

Finally, draw a straight line through these two points.
That's it!
You've graphed the line using its intercepts.

STEP 11

Intercepts give us a quick and easy way to graph a line.
We only need two points to define a line, and the intercepts are often easy to calculate.

STEP 12

In real-world problems, the intercepts can have important meanings.
For example, if x represents time and y represents distance, the y-intercept could be the starting distance, and the x-intercept could be the time it takes to reach a distance of zero.

STEP 13

Intercepts can also help us understand the behavior of a linear function.
The x-intercept tells us where the function equals zero, which can be important in many applications.

STEP 14

We found that the x-intercept is found by setting $\ y = 0$ and solving for $\ x$ .
We graphed a line using its intercepts by finding both the x-intercept and y-intercept, plotting them, and drawing a line through them.
Finally, we saw that intercepts are useful for graphing, interpreting real-world problems, and understanding function behavior.

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QuestionExplain the process of finding the $x$ -intercept of a linear equation.
Describe how you would graph a linear function using its intercepts.
Why is it useful to know the intercepts of a linear function?

Studdy Solution

STEP 1

What is this asking? We need to explain how to find the x-intercept of a line, how to graph a line using its intercepts, and why knowing the intercepts is helpful! Watch out! Don't mix up the x-intercept and the y-intercept!

STEP 2

1. Find the x-intercept
2. Graph using intercepts
3. Why intercepts are useful

STEP 3

To **find the x-intercept** of a linear equation, we need to figure out where the line crosses the x-axis.
Remember, the x-axis is where the y-value is zero!

STEP 4

So, we set $\ y = 0$ in our linear equation.
Let's say our equation is $y = 2x + 4$ .
Substituting $\ y = 0$ , we get $0 = 2x + 4$ .

STEP 5

Now, we solve for $\ x$ .
Subtracting 4 from both sides gives us $-4 = 2x$ .
Then, dividing both sides by 2 gives us $x = -2$ .

STEP 6

So, our x-intercept is $\ (-2, 0)$ .
Remember, it's a point, an address on the graph, not just a number!

STEP 7

To graph a line using its intercepts, we need both the x-intercept and the y-intercept.
We already know how to find the x-intercept.
The y-intercept is where the line crosses the y-axis, so $\ x = 0$ .

STEP 8

Let's use our example equation, $y = 2x + 4$ . Set $\ x = 0$ to get $y = 2 \cdot 0 + 4$ , which simplifies to $y = 4$ .
So, our y-intercept is $\ (0, 4)$ .

STEP 9

Now, we have two points: the x-intercept $\ (-2, 0)$ and the y-intercept $\ (0, 4)$ . Plot these two points on a graph.

STEP 10

Finally, draw a straight line through these two points.
That's it!
You've graphed the line using its intercepts.

STEP 11

Intercepts give us a quick and easy way to graph a line.
We only need two points to define a line, and the intercepts are often easy to calculate.

STEP 12

In real-world problems, the intercepts can have important meanings.
For example, if x represents time and y represents distance, the y-intercept could be the starting distance, and the x-intercept could be the time it takes to reach a distance of zero.

STEP 13

Intercepts can also help us understand the behavior of a linear function.
The x-intercept tells us where the function equals zero, which can be important in many applications.

STEP 14

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QuestionExplain the process of finding the xxx-intercept of a linear equation.Describe how you would graph a linear function using its intercepts.Why is it useful to know the intercepts of a linear function?

Studdy Solution

STEP 1

What is this asking? We need to explain how to find the *x*-intercept of a line, how to graph a line using its intercepts, and why knowing the intercepts is helpful! Watch out! Don't mix up the *x*-intercept and the *y*-intercept!

STEP 2

1. Find the *x*-intercept2. Graph using intercepts3. Why intercepts are useful

STEP 3

To **find the *x*-intercept** of a linear equation, we need to figure out where the line crosses the *x*-axis.Remember, the *x*-axis is where the *y*-value is **zero**!

STEP 4

So, we **set** y=0\ y = 0 y=0 in our linear equation.Let's say our equation is y=2x+4 y = 2x + 4 y=2x+4.Substituting y=0\ y = 0 y=0, we get 0=2x+4 0 = 2x + 4 0=2x+4.

STEP 5

Now, we **solve for** x\ x x.Subtracting 4 from both sides gives us −4=2x -4 = 2x −4=2x.Then, dividing both sides by 2 gives us x=−2 x = -2 x=−2.

STEP 6

So, our *x*-intercept is (−2,0)\ (-2, 0) (−2,0).Remember, it's a point, an address on the graph, not just a number!

STEP 7

To **graph a line using its intercepts**, we need both the *x*-intercept and the *y*-intercept.We already know how to find the *x*-intercept.The *y*-intercept is where the line crosses the *y*-axis, so x=0\ x = 0 x=0.

STEP 8

Let's use our example equation, y=2x+4 y = 2x + 4 y=2x+4. **Set** x=0\ x = 0 x=0 to get y=2⋅0+4 y = 2 \cdot 0 + 4 y=2⋅0+4, which simplifies to y=4 y = 4 y=4.So, our *y*-intercept is (0,4)\ (0, 4) (0,4).

STEP 9

Now, we have two points: the *x*-intercept (−2,0)\ (-2, 0) (−2,0) and the *y*-intercept (0,4)\ (0, 4) (0,4). **Plot these two points** on a graph.

STEP 10

Finally, **draw a straight line** through these two points.That's it!You've graphed the line using its intercepts.

STEP 11

Intercepts give us a **quick and easy way to graph a line**.We only need two points to define a line, and the intercepts are often easy to calculate.

STEP 12

In real-world problems, the intercepts can have **important meanings**.For example, if *x* represents time and *y* represents distance, the *y*-intercept could be the **starting distance**, and the *x*-intercept could be the **time it takes to reach a distance of zero**.

STEP 13

Intercepts can also help us **understand the behavior of a linear function**.The *x*-intercept tells us where the function equals zero, which can be important in many applications.

STEP 14

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionExplain the process of finding the $x$ -intercept of a linear equation.
Describe how you would graph a linear function using its intercepts.
Why is it useful to know the intercepts of a linear function?

What is this asking? We need to explain how to find the x-intercept of a line, how to graph a line using its intercepts, and why knowing the intercepts is helpful! Watch out! Don't mix up the x-intercept and the y-intercept!

1. Find the x-intercept
2. Graph using intercepts
3. Why intercepts are useful

To **find the x-intercept** of a linear equation, we need to figure out where the line crosses the x-axis.
Remember, the x-axis is where the y-value is zero!

So, we set $\ y = 0$ in our linear equation.
Let's say our equation is $y = 2x + 4$ .
Substituting $\ y = 0$ , we get $0 = 2x + 4$ .

Now, we solve for $\ x$ .
Subtracting 4 from both sides gives us $-4 = 2x$ .
Then, dividing both sides by 2 gives us $x = -2$ .

So, our x-intercept is $\ (-2, 0)$ .
Remember, it's a point, an address on the graph, not just a number!

To graph a line using its intercepts, we need both the x-intercept and the y-intercept.
We already know how to find the x-intercept.
The y-intercept is where the line crosses the y-axis, so $\ x = 0$ .

Let's use our example equation, $y = 2x + 4$ . Set $\ x = 0$ to get $y = 2 \cdot 0 + 4$ , which simplifies to $y = 4$ .
So, our y-intercept is $\ (0, 4)$ .

Now, we have two points: the x-intercept $\ (-2, 0)$ and the y-intercept $\ (0, 4)$ . Plot these two points on a graph.

Finally, draw a straight line through these two points.
That's it!
You've graphed the line using its intercepts.

Intercepts give us a quick and easy way to graph a line.
We only need two points to define a line, and the intercepts are often easy to calculate.

In real-world problems, the intercepts can have important meanings.
For example, if x represents time and y represents distance, the y-intercept could be the starting distance, and the x-intercept could be the time it takes to reach a distance of zero.

Intercepts can also help us understand the behavior of a linear function.
The x-intercept tells us where the function equals zero, which can be important in many applications.