QuestionFind the slope and $y$ -intercept of the line given by $-3x - 5y = -20$ . Then, graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as $-3x -5y = -20$ . The equation of a line can be written in the form $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.
3. The slope of the line is the coefficient of $x$ when the equation is in the form $y = mx + c$ .
4. The y-intercept of the line is the constant term when the equation is in the form $y = mx + c$ .

STEP 2

First, we need to rearrange the given equation into the form $y = mx + c$ .
$-x -5y = -20$

STEP 3

Divide the entire equation by $-5$ to isolate $y$ on one side.
$y = \frac{3}{5}x +$

STEP 4

Now that we have the equation in the form $y = mx + c$ , we can identify the slope and the y-intercept. The slope $m$ is the coefficient of $x$ and the y-intercept $c$ is the constant term.

STEP 5

Identify the slope $m$ .
$m = \frac{3}{5}$

STEP 6

Identify the y-intercept $c$ .
$c =4$

STEP 7

Now that we have the slope and the y-intercept, we can use them to graph the line. The y-intercept is the point where the line crosses the y-axis, so we start by putting a point at $(0,4)$ on the graph.

STEP 8

The slope is the rise over the run, which means we go up3 units and move to the right5 units from the y-intercept to plot the next point. Repeat this process to plot several points that lie on the line.

STEP 9

Draw a straight line that passes through all the points plotted.
The slope of the line is $\frac{3}{5}$ and the y-intercept is $4$ . The graph of the line passes through the points plotted using the slope and the y-intercept.

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QuestionFind the slope and $y$ -intercept of the line given by $-3x - 5y = -20$ . Then, graph the line.

Studdy Solution

STEP 1

STEP 2

First, we need to rearrange the given equation into the form $y = mx + c$ .
$-x -5y = -20$

STEP 3

Divide the entire equation by $-5$ to isolate $y$ on one side.
$y = \frac{3}{5}x +$

STEP 4

Now that we have the equation in the form $y = mx + c$ , we can identify the slope and the y-intercept. The slope $m$ is the coefficient of $x$ and the y-intercept $c$ is the constant term.

STEP 5

Identify the slope $m$ .
$m = \frac{3}{5}$

STEP 6

Identify the y-intercept $c$ .
$c =4$

STEP 7

Now that we have the slope and the y-intercept, we can use them to graph the line. The y-intercept is the point where the line crosses the y-axis, so we start by putting a point at $(0,4)$ on the graph.

STEP 8

The slope is the rise over the run, which means we go up3 units and move to the right5 units from the y-intercept to plot the next point. Repeat this process to plot several points that lie on the line.

STEP 9

Draw a straight line that passes through all the points plotted.
The slope of the line is $\frac{3}{5}$ and the y-intercept is $4$ . The graph of the line passes through the points plotted using the slope and the y-intercept.

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QuestionFind the slope and yyy-intercept of the line given by −3x−5y=−20-3x - 5y = -20−3x−5y=−20. Then, graph the line.

Studdy Solution

STEP 1

STEP 2

First, we need to rearrange the given equation into the form y=mx+cy = mx + cy=mx+c.−x−5y=−20-x -5y = -20−x−5y=−20

STEP 3

Divide the entire equation by −5-5−5 to isolate yyy on one side.y=35x+y = \frac{3}{5}x +y=53​x+

STEP 4

Now that we have the equation in the form y=mx+cy = mx + cy=mx+c, we can identify the slope and the y-intercept. The slope mmm is the coefficient of xxx and the y-intercept ccc is the constant term.

STEP 5

Identify the slope mmm.m=35m = \frac{3}{5}m=53​

STEP 6

Identify the y-intercept ccc.c=4c =4c=4

STEP 7

Now that we have the slope and the y-intercept, we can use them to graph the line. The y-intercept is the point where the line crosses the y-axis, so we start by putting a point at (0,4)(0,4)(0,4) on the graph.

STEP 8

The slope is the rise over the run, which means we go up3 units and move to the right5 units from the y-intercept to plot the next point. Repeat this process to plot several points that lie on the line.

STEP 9

Draw a straight line that passes through all the points plotted.The slope of the line is 35\frac{3}{5}53​ and the y-intercept is 444. The graph of the line passes through the points plotted using the slope and the y-intercept.

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

QuestionFind the slope and $y$ -intercept of the line given by $-3x - 5y = -20$ . Then, graph the line.

First, we need to rearrange the given equation into the form $y = mx + c$ .
$-x -5y = -20$

Divide the entire equation by $-5$ to isolate $y$ on one side.
$y = \frac{3}{5}x +$

Now that we have the equation in the form $y = mx + c$ , we can identify the slope and the y-intercept. The slope $m$ is the coefficient of $x$ and the y-intercept $c$ is the constant term.

Identify the slope $m$ .
$m = \frac{3}{5}$

Identify the y-intercept $c$ .
$c =4$

Now that we have the slope and the y-intercept, we can use them to graph the line. The y-intercept is the point where the line crosses the y-axis, so we start by putting a point at $(0,4)$ on the graph.

Draw a straight line that passes through all the points plotted.
The slope of the line is $\frac{3}{5}$ and the y-intercept is $4$ . The graph of the line passes through the points plotted using the slope and the y-intercept.