Linear Equations in Standard Form

Question

Find the equation of a line that contains the points (−8,−1) and (−1,−2).

(Write the equation in standard form.)

Answer 1

Hello Shakevia,

You could find the equation in slope-point form, then convert it into standard form.

1st, you want to find the slope m: m = (y2-y1)/(x2-x1) = (-2+1)/(-1+8) = -1/7

For the point slope, you can use either point. Let's use (-8,-1)

Point-slope equation: y + 1 = (-1/7)* (x+8)

Now to convert it into standard form:

1. multiply both sides by 7: 7*(y+1) = 7*(-1/7)*(x+8) ----> 7y + 7 = -1*(x+8) ----> 7y + 7 = -x - 8
2. Add x to both sides: x + 7y + 7 = -8
3. Subtract 7 from both sides: x + 7y = -15

This should be the answer, but let's check by plugging in the points given to you:

(-8,-1): -8 +7(-1) = -15 ----> check successful

(-1,-2): -1 +7*(-2) = -1 + (-14) = -15 -----> check successful

So the linear equation in standard form is: x + 7y = -15