Find an equation for the line with the given properties. Express the equation in slope-intercept form.

Question

Slope = -3; containing the point (-9,7).

What is the equation of the Line?

y =

Answer 1

Solution:

using slope form the slope of the line is m =-3 . The line passes through point (-9, 7) , ( x₀,y₀)

m = y -y₀/ x-x₀ , -3 = (y-7) / (x-(-9)) , -3 = (y-7) / (x+9) cross multiply

y-7 = -3(x+9), y-7 = -3x -27 , y = -3x -27 + 7 , y = -3x -20 this can also be written as y = mx + b in slope intercept form where m =-3, and b =-20 note that the point (0,-20) is the y intercept point and can be easily found from the equation y = -3x -20. for x =0, y= -3(0) -20 , y=-20

Answer 2

1. Slope = (y - y₁)/(x - x₁),
2. Slope = -3, x₁ = -9, y₁ = 7 (Given)
3. -3 = (y - (-9))/(x - 7),
4. -3 = (y + 9) / (x -7),
5. -3 * (x - 7) = y + 9,
6. -3x +21 = y +9
7. -3x +21 - 9 = y
8. y = -3x + 12 The equation of the Line.