Math / Algebra

QuestionQuestion Graph the line with the equation $y = \frac{2}{5}x + 1$ .

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation $y = \frac{2}{5}x + 1$ . Watch out! Don't mix up the slope and the y-intercept!

STEP 2

1. Find the y-intercept.
2. Find the slope.
3. Plot the y-intercept.
4. Use the slope to find another point.
5. Draw the line.

STEP 3

The y-intercept is the value of $y$ when $x = 0$ .
Let's substitute $x = 0$ into our equation: $y = \frac{2}{5} \cdot 0 + 1$

STEP 4

Any number multiplied by zero is zero, so $\frac{2}{5} \cdot 0 = 0$ . $y = 0 + 1$

STEP 5

Adding zero to a number doesn't change the number, so $0 + 1 = 1$ . $y = 1$

STEP 6

So, our y-intercept is $1$ , which means the line crosses the y-axis at the point $(0, 1)$ .

STEP 7

Our equation is in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 8

In our equation, $y = \frac{2}{5}x + 1$ , the slope $m$ is $\frac{2}{5}$ .
This tells us that for every 5 units we move to the right along the x-axis, we move 2 units up along the y-axis.

STEP 9

We found that the y-intercept is $(0, 1)$ .
So, let's put a point at $(0, 1)$ on our graph!

STEP 10

Starting from our y-intercept $(0, 1)$ , we can use the slope $\frac{2}{5}$ to find another point.

STEP 11

The slope tells us to move 5 units to the right ( $+5$ to the $x$ -value) and 2 units up ( $+2$ to the $y$ -value).

STEP 12

Starting at $(0, 1)$ , adding $5$ to $x$ gives us $0 + 5 = 5$ , and adding $2$ to $y$ gives us $1 + 2 = 3$ .

STEP 13

So, our second point is $(5, 3)$ .
Let's plot this point on the graph!

STEP 14

Now that we have two points, $(0, 1)$ and $(5, 3)$ , we can draw a straight line through them.
Extend the line in both directions to show that it continues infinitely.

STEP 15

The graph of the line $y = \frac{2}{5}x + 1$ is a straight line passing through the points $(0, 1)$ and $(5, 3)$ .

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QuestionQuestion Graph the line with the equation $y = \frac{2}{5}x + 1$ .

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation $y = \frac{2}{5}x + 1$ . Watch out! Don't mix up the slope and the y-intercept!

STEP 2

1. Find the y-intercept.
2. Find the slope.
3. Plot the y-intercept.
4. Use the slope to find another point.
5. Draw the line.

STEP 3

The y-intercept is the value of $y$ when $x = 0$ .
Let's substitute $x = 0$ into our equation: $y = \frac{2}{5} \cdot 0 + 1$

STEP 4

Any number multiplied by zero is zero, so $\frac{2}{5} \cdot 0 = 0$ . $y = 0 + 1$

STEP 5

Adding zero to a number doesn't change the number, so $0 + 1 = 1$ . $y = 1$

STEP 6

So, our y-intercept is $1$ , which means the line crosses the y-axis at the point $(0, 1)$ .

STEP 7

Our equation is in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 8

In our equation, $y = \frac{2}{5}x + 1$ , the slope $m$ is $\frac{2}{5}$ .
This tells us that for every 5 units we move to the right along the x-axis, we move 2 units up along the y-axis.

STEP 9

We found that the y-intercept is $(0, 1)$ .
So, let's put a point at $(0, 1)$ on our graph!

STEP 10

Starting from our y-intercept $(0, 1)$ , we can use the slope $\frac{2}{5}$ to find another point.

STEP 11

The slope tells us to move 5 units to the right ( $+5$ to the $x$ -value) and 2 units up ( $+2$ to the $y$ -value).

STEP 12

Starting at $(0, 1)$ , adding $5$ to $x$ gives us $0 + 5 = 5$ , and adding $2$ to $y$ gives us $1 + 2 = 3$ .

STEP 13

So, our second point is $(5, 3)$ .
Let's plot this point on the graph!

STEP 14

Now that we have two points, $(0, 1)$ and $(5, 3)$ , we can draw a straight line through them.
Extend the line in both directions to show that it continues infinitely.

STEP 15

The graph of the line $y = \frac{2}{5}x + 1$ is a straight line passing through the points $(0, 1)$ and $(5, 3)$ .

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QuestionQuestion Graph the line with the equation y=25x+1y = \frac{2}{5}x + 1y=52​x+1.

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation y=25x+1y = \frac{2}{5}x + 1y=52​x+1. Watch out! Don't mix up the **slope** and the **y-intercept**!

STEP 2

1. Find the y-intercept.2. Find the slope.3. Plot the y-intercept.4. Use the slope to find another point.5. Draw the line.

STEP 3

The **y-intercept** is the value of yyy when x=0x = 0x=0.Let's **substitute** x=0x = 0x=0 into our equation: y=25⋅0+1y = \frac{2}{5} \cdot 0 + 1y=52​⋅0+1

STEP 4

Any number multiplied by zero is zero, so 25⋅0=0\frac{2}{5} \cdot 0 = 052​⋅0=0. y=0+1y = 0 + 1y=0+1

STEP 5

Adding zero to a number doesn't change the number, so 0+1=10 + 1 = 10+1=1. y=1y = 1y=1

STEP 6

So, our **y-intercept** is 111, which means the line crosses the y-axis at the point (0,1)(0, 1)(0,1).

STEP 7

Our equation is in **slope-intercept form**, which is y=mx+by = mx + by=mx+b, where mmm is the **slope** and bbb is the **y-intercept**.

STEP 8

In our equation, y=25x+1y = \frac{2}{5}x + 1y=52​x+1, the **slope** mmm is 25\frac{2}{5}52​.This tells us that for every **5** units we move to the right along the x-axis, we move **2** units up along the y-axis.

STEP 9

We found that the **y-intercept** is (0,1)(0, 1)(0,1).So, let's put a point at (0,1)(0, 1)(0,1) on our graph!

STEP 10

Starting from our **y-intercept** (0,1)(0, 1)(0,1), we can use the **slope** 25\frac{2}{5}52​ to find another point.

STEP 11

The **slope** tells us to move **5** units to the right (+5+5+5 to the xxx-value) and **2** units up (+2+2+2 to the yyy-value).

STEP 12

Starting at (0,1)(0, 1)(0,1), adding 555 to xxx gives us 0+5=50 + 5 = 50+5=5, and adding 222 to yyy gives us 1+2=31 + 2 = 31+2=3.

STEP 13

So, our second point is (5,3)(5, 3)(5,3).Let's plot this point on the graph!

STEP 14

Now that we have two points, (0,1)(0, 1)(0,1) and (5,3)(5, 3)(5,3), we can draw a straight line through them.Extend the line in both directions to show that it continues infinitely.

STEP 15

The graph of the line y=25x+1y = \frac{2}{5}x + 1y=52​x+1 is a straight line passing through the points (0,1)(0, 1)(0,1) and (5,3)(5, 3)(5,3).

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QuestionQuestion Graph the line with the equation $y = \frac{2}{5}x + 1$ .

What is this asking? Draw the line represented by the equation $y = \frac{2}{5}x + 1$ . Watch out! Don't mix up the slope and the y-intercept!

1. Find the y-intercept.
2. Find the slope.
3. Plot the y-intercept.
4. Use the slope to find another point.
5. Draw the line.

The y-intercept is the value of $y$ when $x = 0$ .
Let's substitute $x = 0$ into our equation: $y = \frac{2}{5} \cdot 0 + 1$

Any number multiplied by zero is zero, so $\frac{2}{5} \cdot 0 = 0$ . $y = 0 + 1$

Adding zero to a number doesn't change the number, so $0 + 1 = 1$ . $y = 1$

So, our y-intercept is $1$ , which means the line crosses the y-axis at the point $(0, 1)$ .

Our equation is in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

In our equation, $y = \frac{2}{5}x + 1$ , the slope $m$ is $\frac{2}{5}$ .
This tells us that for every 5 units we move to the right along the x-axis, we move 2 units up along the y-axis.

We found that the y-intercept is $(0, 1)$ .
So, let's put a point at $(0, 1)$ on our graph!

Starting from our y-intercept $(0, 1)$ , we can use the slope $\frac{2}{5}$ to find another point.

The slope tells us to move 5 units to the right ( $+5$ to the $x$ -value) and 2 units up ( $+2$ to the $y$ -value).

Starting at $(0, 1)$ , adding $5$ to $x$ gives us $0 + 5 = 5$ , and adding $2$ to $y$ gives us $1 + 2 = 3$ .

So, our second point is $(5, 3)$ .
Let's plot this point on the graph!

Now that we have two points, $(0, 1)$ and $(5, 3)$ , we can draw a straight line through them.
Extend the line in both directions to show that it continues infinitely.

The graph of the line $y = \frac{2}{5}x + 1$ is a straight line passing through the points $(0, 1)$ and $(5, 3)$ .