Pre-Calculus: Writing Linear Equations

Question

Write an equation in slope-intercept form of the line that has slope -4 and passes through the point at (2,-2).

Answer 1

The best method to use here would be to use algebra to convert the point-slope form available from the given information to slope-intercept form.

 

If you take the equation for point-slope form (y-y₁) = m(x-x₁) and plug in the known values for slope (-4), x(2), and y(-2), it can be easily rearranged to a point slope form.

 

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

 

-->  Changing the sign for y values gives:           (y + 2) = -4(x - 2) 

 

-->  Factoring in the slope gives:                        y+2 = -4x + 8

 

-->  Subtracting both sides by 2 gives:                y = -4x + 6,

 

So this would be the correct equation in slope-intercept form for an equation with a slope of -4 and a y-intercept of 6.

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