Question

Which equation represents the line that passes through the points (–4, 3) and (2, –12)?

Answer 1

Equation `y = -5/2 x -7`

Explanation:

The slope m = `(y_1 - y_2)/(x_1 - x_2)` Putting in the points gives

m = `( -12 - 3)/(2-( - 4))` This gives m = `-15/6`
Dividing out common factors `(\div 3)` gives m = `-5/2`

Putting this value in for m in the y = mx + b gives `\color(blue)(y) = -5/2\color(red)(x) + b`
Now substitute one set of point values
`\color(blue)(3)= -5/2(\color(red)(-4)) + b`
solving for b gives `3 = 10 + b`
subtract 10 from both sides `3- 10 = 10-10 + b`
`-7 = b`

`\therefore y = -5/2 x -7`