QuestionFind the point-slope and slope-intercept forms of the line through $(-2,0)$ and $(0,6)$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the points $(-,0)$ and $(0,6)$ . We need to find the point-slope form and the slope-intercept form of the line

STEP 2

First, we need to find the slope of the line. The slope (m) is calculated as the change in y divided by the change in x.
$m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{6 -0}{0 - (-2)}$

STEP 4

Calculate the slope.
$m = \frac{6}{2} =3$

STEP 5

Now that we have the slope, we can write the point-slope form of the line. The point-slope form is $y - y1 = m(x - x1)$ .

STEP 6

Plug in the values for $m$ , $x1$ , and $y1$ to write the point-slope form of the line.
$y -0 =3(x - (-2))$

STEP 7

implify the equation to get the point-slope form of the line.
$y =3(x +2)$

STEP 8

Now that we have the point-slope form of the line, we can write the slope-intercept form of the line. The slope-intercept form is $y = mx + b$ .

STEP 9

We already know the slope (m), so we just need to find the y-intercept (b). We can do this by plugging in the values for $x$ and $y$ from one of the given points and solving for $b$ .
$=3(-2) + b$

STEP 10

olve for $b$ .
$b =0 -3(-2) =6$

STEP 11

Now that we have the y-intercept, we can write the slope-intercept form of the line.
$y =3x +6$ The point-slope form of the line is $y =3(x +)$ and the slope-intercept form of the line is $y =3x +6$ .

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QuestionFind the point-slope and slope-intercept forms of the line through $(-2,0)$ and $(0,6)$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the points $(-,0)$ and $(0,6)$ . We need to find the point-slope form and the slope-intercept form of the line

STEP 2

First, we need to find the slope of the line. The slope (m) is calculated as the change in y divided by the change in x.
$m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{6 -0}{0 - (-2)}$

STEP 4

Calculate the slope.
$m = \frac{6}{2} =3$

STEP 5

Now that we have the slope, we can write the point-slope form of the line. The point-slope form is $y - y1 = m(x - x1)$ .

STEP 6

Plug in the values for $m$ , $x1$ , and $y1$ to write the point-slope form of the line.
$y -0 =3(x - (-2))$

STEP 7

implify the equation to get the point-slope form of the line.
$y =3(x +2)$

STEP 8

Now that we have the point-slope form of the line, we can write the slope-intercept form of the line. The slope-intercept form is $y = mx + b$ .

STEP 9

We already know the slope (m), so we just need to find the y-intercept (b). We can do this by plugging in the values for $x$ and $y$ from one of the given points and solving for $b$ .
$=3(-2) + b$

STEP 10

olve for $b$ .
$b =0 -3(-2) =6$

STEP 11

Now that we have the y-intercept, we can write the slope-intercept form of the line.
$y =3x +6$ The point-slope form of the line is $y =3(x +)$ and the slope-intercept form of the line is $y =3x +6$ .

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QuestionFind the point-slope and slope-intercept forms of the line through (−2,0)(-2,0)(−2,0) and (0,6)(0,6)(0,6).

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (−,0)(-,0)(−,0) and (0,6)(0,6)(0,6). We need to find the point-slope form and the slope-intercept form of the line

STEP 2

First, we need to find the slope of the line. The slope (m) is calculated as the change in y divided by the change in x.m=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Now, plug in the given values for x1x1x1, y1y1y1, x2x2x2, and y2y2y2 to calculate the slope.m=6−00−(−2)m = \frac{6 -0}{0 - (-2)}m=0−(−2)6−0​

STEP 4

Calculate the slope.m=62=3m = \frac{6}{2} =3m=26​=3

STEP 5

Now that we have the slope, we can write the point-slope form of the line. The point-slope form is y−y1=m(x−x1)y - y1 = m(x - x1)y−y1=m(x−x1).

STEP 6

Plug in the values for mmm, x1x1x1, and y1y1y1 to write the point-slope form of the line.y−0=3(x−(−2))y -0 =3(x - (-2))y−0=3(x−(−2))

STEP 7

implify the equation to get the point-slope form of the line.y=3(x+2)y =3(x +2)y=3(x+2)

STEP 8

Now that we have the point-slope form of the line, we can write the slope-intercept form of the line. The slope-intercept form is y=mx+by = mx + by=mx+b.

STEP 9

We already know the slope (m), so we just need to find the y-intercept (b). We can do this by plugging in the values for xxx and yyy from one of the given points and solving for bbb.=3(−2)+b =3(-2) + b=3(−2)+b

STEP 10

olve for bbb.b=0−3(−2)=6b =0 -3(-2) =6b=0−3(−2)=6

STEP 11

Now that we have the y-intercept, we can write the slope-intercept form of the line.y=3x+6y =3x +6y=3x+6The point-slope form of the line is y=3(x+)y =3(x +)y=3(x+) and the slope-intercept form of the line is y=3x+6y =3x +6y=3x+6.

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QuestionFind the point-slope and slope-intercept forms of the line through $(-2,0)$ and $(0,6)$ .

Assumptions1. The line passes through the points $(-,0)$ and $(0,6)$ . We need to find the point-slope form and the slope-intercept form of the line

First, we need to find the slope of the line. The slope (m) is calculated as the change in y divided by the change in x.
$m = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{6 -0}{0 - (-2)}$

Calculate the slope.
$m = \frac{6}{2} =3$

Now that we have the slope, we can write the point-slope form of the line. The point-slope form is $y - y1 = m(x - x1)$ .

Plug in the values for $m$ , $x1$ , and $y1$ to write the point-slope form of the line.
$y -0 =3(x - (-2))$

implify the equation to get the point-slope form of the line.
$y =3(x +2)$

Now that we have the point-slope form of the line, we can write the slope-intercept form of the line. The slope-intercept form is $y = mx + b$ .

We already know the slope (m), so we just need to find the y-intercept (b). We can do this by plugging in the values for $x$ and $y$ from one of the given points and solving for $b$ .
$=3(-2) + b$

olve for $b$ .
$b =0 -3(-2) =6$

Now that we have the y-intercept, we can write the slope-intercept form of the line.
$y =3x +6$ The point-slope form of the line is $y =3(x +)$ and the slope-intercept form of the line is $y =3x +6$ .