QuestionFind the slope and $y$ -intercept of the line given by $-2x + 5y = -5$ , then graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as $-x +5y = -5$ . . We need to find the slope and the y-intercept of the line.
3. The equation of a line can be written in the slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

First, we need to rewrite the given equation in the slope-intercept form. We can do this by isolating $y$ on one side of the equation.
$-2x +5y = -5$ $5y =2x -5$

STEP 3

Now, divide every term by5 to solve for $y$ .
$y = \frac{2}{5}x -1$

STEP 4

Now that we have the equation in slope-intercept form, we can identify the slope and the y-intercept.The slope $m$ is the coefficient of $x$ , and the y-intercept $b$ is the constant term.
In our equation, $y = \frac{2}{}x -1$ , the slope $m$ is $\frac{2}{}$ and the y-intercept $b$ is $-1$ .

STEP 5

To graph the line, we first plot the y-intercept on the y-axis. The y-intercept is $-1$ , so we plot a point at $(0, -1)$ .

STEP 6

The slope is $\frac{2}{5}$ , which means that for every5 units we move to the right on the x-axis, we move2 units up on the y-axis. Starting from the y-intercept, we can use the slope to find another point on the line.If we move5 units to the right from $(0, -1)$ , we arrive at $(5, -1)$ . From here, we move2 units up to get to the point $(5,1)$ .

STEP 7

Now that we have two points, $(0, -1)$ and $(5,1)$ , we can draw a line through these points to graph the line.
The slope of the line is $\frac{2}{5}$ and the y-intercept is $-1$ .

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QuestionFind the slope and $y$ -intercept of the line given by $-2x + 5y = -5$ , then graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as $-x +5y = -5$ . . We need to find the slope and the y-intercept of the line.
3. The equation of a line can be written in the slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

First, we need to rewrite the given equation in the slope-intercept form. We can do this by isolating $y$ on one side of the equation.
$-2x +5y = -5$ $5y =2x -5$

STEP 3

Now, divide every term by5 to solve for $y$ .
$y = \frac{2}{5}x -1$

STEP 4

Now that we have the equation in slope-intercept form, we can identify the slope and the y-intercept.The slope $m$ is the coefficient of $x$ , and the y-intercept $b$ is the constant term.
In our equation, $y = \frac{2}{}x -1$ , the slope $m$ is $\frac{2}{}$ and the y-intercept $b$ is $-1$ .

STEP 5

To graph the line, we first plot the y-intercept on the y-axis. The y-intercept is $-1$ , so we plot a point at $(0, -1)$ .

STEP 6

STEP 7

Now that we have two points, $(0, -1)$ and $(5,1)$ , we can draw a line through these points to graph the line.
The slope of the line is $\frac{2}{5}$ and the y-intercept is $-1$ .

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QuestionFind the slope and yyy-intercept of the line given by −2x+5y=−5-2x + 5y = -5−2x+5y=−5, then graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as −x+5y=−5-x +5y = -5−x+5y=−5. . We need to find the slope and the y-intercept of the line.3. The equation of a line can be written in the slope-intercept form, y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

First, we need to rewrite the given equation in the slope-intercept form. We can do this by isolating yyy on one side of the equation.−2x+5y=−5-2x +5y = -5−2x+5y=−55y=2x−55y =2x -55y=2x−5

STEP 3

Now, divide every term by5 to solve for yyy.y=25x−1y = \frac{2}{5}x -1y=52​x−1

STEP 4

STEP 5

To graph the line, we first plot the y-intercept on the y-axis. The y-intercept is −1-1−1, so we plot a point at (0,−1)(0, -1)(0,−1).

STEP 6

STEP 7

Now that we have two points, (0,−1)(0, -1)(0,−1) and (5,1)(5,1)(5,1), we can draw a line through these points to graph the line.The slope of the line is 25\frac{2}{5}52​ and the y-intercept is −1-1−1.

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QuestionFind the slope and $y$ -intercept of the line given by $-2x + 5y = -5$ , then graph the line.

Assumptions1. The equation of the line is given as $-x +5y = -5$ . . We need to find the slope and the y-intercept of the line.
3. The equation of a line can be written in the slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

First, we need to rewrite the given equation in the slope-intercept form. We can do this by isolating $y$ on one side of the equation.
$-2x +5y = -5$ $5y =2x -5$

Now, divide every term by5 to solve for $y$ .
$y = \frac{2}{5}x -1$

To graph the line, we first plot the y-intercept on the y-axis. The y-intercept is $-1$ , so we plot a point at $(0, -1)$ .

Now that we have two points, $(0, -1)$ and $(5,1)$ , we can draw a line through these points to graph the line.
The slope of the line is $\frac{2}{5}$ and the y-intercept is $-1$ .