How to solve it?

Question

Write a equation of the line through the points (-6,-19) and (2,5)

Answer 1

Given the points:

1. (x₁, y₁) = (-6, -19)
2. (x₂, y₂) = (2, 5)

We can find the equation of the line through these points by

1. Calculate the Slope
2. Slope = (y₂ - y₁)/(x₂ - x₁) = (5- -19)/2- -6) = (5+19)/(2+6) = 24/8 = 3
3. Recall that when you subtract a negative number the sign switches to become addition.
4. Use the slope-intercept equation of a line
5. y = mx +b
6. y = 3x +b
7. Now, use one of the points (it really doesn't matter which one so pick one that will make the problem easier for you) to solve for the quantity 'b'
8. 5 = 3(2) + b ..... 5 = 6 +b .... subtract 6 from both sides to get:
9. b = -1
10. Put it all together for the equation of the line:
11. y = 3x - 1

If this was helpful (or not) please leave a comment.

Thank you,

David

Answer 2

First find the slope of the line passing through your two points: change in y values/change in x values

[5 -(-19)]/[2-(-6)]= [5+19]/[2+6]= [24/8] = 3 so m = 3

Select one of the points, I suggest using (2,5) since both values are positive. Substitute 2 in for x, 5 in for y and 3 in for m into y=mx+b 5=3(2) + b multiple 3(2) 5 = 6 + b solve for b b = -1

Substitute m=3 and b= -1 back into y=mx+b y=3x - 1