Question

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

(-2,-3);y=-4x+5

Write an equation for the line in​ slope-intercept form.

​(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)

Answer 1

To find the equation of a line parallel to the given equation, we notice that parallel lines have the same slope. Since the given equation is in slope-intercept form y = mx + b, where m is the slope, we can determine the slope of the given equation as -4.

Now we can use the point-slope form of a linear equation (y - y1) = m(x - x1) and substitute the given point (-2, -3) and slope -4 into the equation:

(y - (-3)) = -4(x - (-2))

Simplifying the equation gives:

y + 3 = -4(x + 2)

Expanding the equation further:

y + 3 = -4x - 8

To get the equation in slope-intercept form, we isolate y on one side of the equation:

y = -4x - 8 - 3

This simplifies to:

y = -4x - 11

Therefore, the equation of the line that passes through the given point (-2,-3) and is parallel to the graph of y = -4x + 5 is y = -4x - 11.