Math / Geometry

QuestionGraph the linear equation using the slope and $y$ -intercept. $y=\frac{1}{3} x+5$

Studdy Solution

STEP 1

What is this asking? Draw a line on a graph that represents the equation $y = \frac{1}{3}x + 5$ . Watch out! Don't mix up the slope and the $y$ -intercept!

STEP 2

1. Identify the slope.
2. Identify the y-intercept.
3. Plot the y-intercept.
4. Use the slope to find a second point.
5. Draw the line.

STEP 3

The slope tells us how steep the line is and in which direction it goes.
In the equation $y = mx + b$ , the slope is represented by $m$ .
Looking at our equation, $y = \frac{1}{3}x + 5$ , we can see that our slope is $m = \frac{1}{3}$ .
This means that for every 1 unit we move to the right on the $x$ -axis (the run), we move 3 units up on the $y$ -axis (the rise).

STEP 4

The $y$ -intercept is where the line crosses the $y$ -axis.
It's the value of $y$ when $x = 0$ .
In the equation $y = mx + b$ , the $y$ -intercept is represented by $b$ .
In our equation, $y = \frac{1}{3}x + 5$ , the $y$ -intercept is $b = 5$ .
This means the line crosses the $y$ -axis at the point $(0, 5)$ .

STEP 5

Let's put a point on our graph at $(0, 5)$ .
This is our starting point!

STEP 6

Remember our slope is $\frac{1}{3}$ .
Starting from our $y$ -intercept $(0, 5)$ , we move 1 unit to the right (run) and 3 units up (rise).
This takes us to the point $(0 + 1, 5 + 3)$ , which simplifies to $(1, 8)$ .

STEP 7

Now that we have two points, $(0, 5)$ and $(1, 8)$ , we can draw a straight line through them.
Extend the line in both directions, because it goes on forever!

STEP 8

The graph of the linear equation $y = \frac{1}{3}x + 5$ is a line that passes through the points $(0, 5)$ and $(1, 8)$ , with a slope of $\frac{1}{3}$ .

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QuestionGraph the linear equation using the slope and $y$ -intercept. $y=\frac{1}{3} x+5$

Studdy Solution

STEP 1

What is this asking? Draw a line on a graph that represents the equation $y = \frac{1}{3}x + 5$ . Watch out! Don't mix up the slope and the $y$ -intercept!

STEP 2

1. Identify the slope.
2. Identify the y-intercept.
3. Plot the y-intercept.
4. Use the slope to find a second point.
5. Draw the line.

STEP 3

STEP 4

STEP 5

Let's put a point on our graph at $(0, 5)$ .
This is our starting point!

STEP 6

Remember our slope is $\frac{1}{3}$ .
Starting from our $y$ -intercept $(0, 5)$ , we move 1 unit to the right (run) and 3 units up (rise).
This takes us to the point $(0 + 1, 5 + 3)$ , which simplifies to $(1, 8)$ .

STEP 7

Now that we have two points, $(0, 5)$ and $(1, 8)$ , we can draw a straight line through them.
Extend the line in both directions, because it goes on forever!

STEP 8

The graph of the linear equation $y = \frac{1}{3}x + 5$ is a line that passes through the points $(0, 5)$ and $(1, 8)$ , with a slope of $\frac{1}{3}$ .

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QuestionGraph the linear equation using the slope and yyy-intercept. y=13x+5y=\frac{1}{3} x+5y=31​x+5

Studdy Solution

STEP 1

What is this asking? Draw a line on a graph that represents the equation y=13x+5y = \frac{1}{3}x + 5y=31​x+5. Watch out! Don't mix up the slope and the yyy-intercept!

STEP 2

1. Identify the slope.2. Identify the y-intercept.3. Plot the y-intercept.4. Use the slope to find a second point.5. Draw the line.

STEP 3

STEP 4

STEP 5

Let's put a point on our graph at (0,5)(0, 5)(0,5).This is our **starting point**!

STEP 6

Remember our **slope** is 13\frac{1}{3}31​.Starting from our **yyy-intercept** (0,5)(0, 5)(0,5), we move **1** unit to the right (run) and **3** units up (rise).This takes us to the point (0+1,5+3)(0 + 1, 5 + 3)(0+1,5+3), which simplifies to (1,8)(1, 8)(1,8).

STEP 7

Now that we have two points, (0,5)(0, 5)(0,5) and (1,8)(1, 8)(1,8), we can draw a straight line through them.Extend the line in both directions, because it goes on forever!

STEP 8

The graph of the linear equation y=13x+5y = \frac{1}{3}x + 5y=31​x+5 is a line that passes through the points (0,5)(0, 5)(0,5) and (1,8)(1, 8)(1,8), with a slope of 13\frac{1}{3}31​.

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QuestionGraph the linear equation using the slope and $y$ -intercept. $y=\frac{1}{3} x+5$

What is this asking? Draw a line on a graph that represents the equation $y = \frac{1}{3}x + 5$ . Watch out! Don't mix up the slope and the $y$ -intercept!

1. Identify the slope.
2. Identify the y-intercept.
3. Plot the y-intercept.
4. Use the slope to find a second point.
5. Draw the line.

Let's put a point on our graph at $(0, 5)$ .
This is our starting point!

Remember our slope is $\frac{1}{3}$ .
Starting from our $y$ -intercept $(0, 5)$ , we move 1 unit to the right (run) and 3 units up (rise).
This takes us to the point $(0 + 1, 5 + 3)$ , which simplifies to $(1, 8)$ .

Now that we have two points, $(0, 5)$ and $(1, 8)$ , we can draw a straight line through them.
Extend the line in both directions, because it goes on forever!

The graph of the linear equation $y = \frac{1}{3}x + 5$ is a line that passes through the points $(0, 5)$ and $(1, 8)$ , with a slope of $\frac{1}{3}$ .