Question

(-4, -2); y = - 2x + 4

Write an equation in slope-intercept form of a line that passed through the given point and is parallel to the graph of the given equation

Answer 1

y = -2x - 10

Explanation:

Slope intercept form of equation is of form

y = mx+c

where m is the slope of line and c is the y intercept of the line.

Y intercept is point on y axis where the line intersects the y axis.

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Given equation

y = -2x +4

comparing it with y = mx+ c

m = -2 , c = 4

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when two lines are parallel, their slopes are equal.

Let the equation of new line in slope intercept form be y = mx + c

Thus slope of of new required line is -2

Thus m for new line is -2.

now, equation of required line : y = -2x+c

Given that this line passes through (-4, -2). This point shall should satisfy equation y = -2x+c.

Substituting the value of (-4, -2) we have

-2 = -2(-4)+c

=> -2 = 8 +c

=> -2 -8 = c

=> c = -10.

Thus , equation of required line is y = -2x - 10.