Question

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Passing through (-7,-6) and parallel to the line whose equation is y = - 2x + 2

Answer 1

y= -2x-20 (point-slope form)

y= -2x-20 (slope-intercept form)

Explanation:

We can construct an equation by using y=mx+c where m is the gradient (slope) and c is the y-intercept. The y-intercept is the point where x is 0.

One of the properties of two parallel lines in a graph is that their gradient is the same. the equation of the other line is already in the form of y=mx+c, y= -2x + 2, so the gradient of the line whose equation is to be found is -2. Next by using y-y1= m(x-x1), we can construct the equation by using the coordinates given in the question.

y-(-6)= -2(x-(-7))

y+6=-2(x+7)

y+6= -2x-14

y= -2x-20

That was the slope-intercept form.

For point-slope form:

y=mx+c

Use the coordinates and gradient to rearrange c and find its value.

-6= -2(-7) + c

-6= 14+c

c= -6-14

c= -20

Now plug in the gradient and the c value into the equation:

y= -2x +(-20)

y= -2x-20