QuestionFind the slope-intercept form of the line through $(-1,5)$ , parallel to $4x+2y=8$ . Choose from A, B, C, D.

Studdy Solution

STEP 1

Assumptions1. We are given a point through which the line passes $(-1,5)$ . We are given a line defined by the equation $4x+y=8$ , and our line is parallel to this line.
3. We need to find the equation of our line in slope-intercept form, which is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

First, we need to find the slope of the given line. We can do this by rearranging the equation into slope-intercept form.
$4x+2y=8$ Rearrange to get $y$ on one side $2y=-4x+8$ Divide by2 to isolate $y$ $y=-2x+4$

STEP 3

The slope of the given line is the coefficient of $x$ , which is $-2$ . Since parallel lines have the same slope, the slope of our line is also $-2$ .

STEP 4

Now that we have the slope, we can use the point-slope form of a line to find the equation of our line. The point-slope form is $y-y1=m(x-x1)$ , where $(x1,y1)$ is a point on the line and $m$ is the slope.

STEP 5

Substitute the given point $(-1,5)$ and the slope $-2$ into the point-slope form $y-5=-2(x-(-1))$

STEP 6

implify the equation $y-5=-2(x+1)$

STEP 7

istribute the $-2$ $y-5=-2x-2$

STEP 8

Add5 to both sides to get the equation in slope-intercept form $y=-2x+3$ The correct equation of the line that passes through the point $(-1,5)$ and is parallel to the line defined by the equation $4x+2y=8$ is $y=-2x+3$ , which corresponds to option D.

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QuestionFind the slope-intercept form of the line through $(-1,5)$ , parallel to $4x+2y=8$ . Choose from A, B, C, D.

Studdy Solution

STEP 1

STEP 2

First, we need to find the slope of the given line. We can do this by rearranging the equation into slope-intercept form.
$4x+2y=8$ Rearrange to get $y$ on one side $2y=-4x+8$ Divide by2 to isolate $y$ $y=-2x+4$

STEP 3

The slope of the given line is the coefficient of $x$ , which is $-2$ . Since parallel lines have the same slope, the slope of our line is also $-2$ .

STEP 4

Now that we have the slope, we can use the point-slope form of a line to find the equation of our line. The point-slope form is $y-y1=m(x-x1)$ , where $(x1,y1)$ is a point on the line and $m$ is the slope.

STEP 5

Substitute the given point $(-1,5)$ and the slope $-2$ into the point-slope form $y-5=-2(x-(-1))$

STEP 6

implify the equation $y-5=-2(x+1)$

STEP 7

istribute the $-2$ $y-5=-2x-2$

STEP 8

Add5 to both sides to get the equation in slope-intercept form $y=-2x+3$ The correct equation of the line that passes through the point $(-1,5)$ and is parallel to the line defined by the equation $4x+2y=8$ is $y=-2x+3$ , which corresponds to option D.

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QuestionFind the slope-intercept form of the line through (−1,5)(-1,5)(−1,5), parallel to 4x+2y=84x+2y=84x+2y=8. Choose from A, B, C, D.

Studdy Solution

STEP 1

STEP 2

First, we need to find the slope of the given line. We can do this by rearranging the equation into slope-intercept form.4x+2y=84x+2y=84x+2y=8Rearrange to get yyy on one side2y=−4x+82y=-4x+82y=−4x+8Divide by2 to isolate yyyy=−2x+4y=-2x+4y=−2x+4

STEP 3

The slope of the given line is the coefficient of xxx, which is −2-2−2. Since parallel lines have the same slope, the slope of our line is also −2-2−2.

STEP 4

Now that we have the slope, we can use the point-slope form of a line to find the equation of our line. The point-slope form is y−y1=m(x−x1)y-y1=m(x-x1)y−y1=m(x−x1), where (x1,y1)(x1,y1)(x1,y1) is a point on the line and mmm is the slope.

STEP 5

Substitute the given point (−1,5)(-1,5)(−1,5) and the slope −2-2−2 into the point-slope formy−5=−2(x−(−1))y-5=-2(x-(-1))y−5=−2(x−(−1))

STEP 6

implify the equationy−5=−2(x+1)y-5=-2(x+1)y−5=−2(x+1)

STEP 7

istribute the −2-2−2y−5=−2x−2y-5=-2x-2y−5=−2x−2

STEP 8

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QuestionFind the slope-intercept form of the line through $(-1,5)$ , parallel to $4x+2y=8$ . Choose from A, B, C, D.

First, we need to find the slope of the given line. We can do this by rearranging the equation into slope-intercept form.
$4x+2y=8$ Rearrange to get $y$ on one side $2y=-4x+8$ Divide by2 to isolate $y$ $y=-2x+4$

The slope of the given line is the coefficient of $x$ , which is $-2$ . Since parallel lines have the same slope, the slope of our line is also $-2$ .

Now that we have the slope, we can use the point-slope form of a line to find the equation of our line. The point-slope form is $y-y1=m(x-x1)$ , where $(x1,y1)$ is a point on the line and $m$ is the slope.

Substitute the given point $(-1,5)$ and the slope $-2$ into the point-slope form $y-5=-2(x-(-1))$

implify the equation $y-5=-2(x+1)$

istribute the $-2$ $y-5=-2x-2$