Question

What is an equation of the line that passes through the points (-4,-5) and (-8, -2)?

Answer 1

Step-by-step explanation:

first we need to find the slope of the line.

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to the other.

we see here

x changes by -4 (from -4 to -8).

y changes by +3 (from -5 to -2).

so, the slope is +3/-4 = -3/4

there are two main forms for the equation of a line :

the slope-intercept form

y = ax + b

and the point-slope form

y - y1 = a(x - x1)

where "a" is the slope, and (x1, y1) is a point on the line.

we can pick any point, and I would pick (-4, -5).

so we get as point-slope form

y + 5 = -3/4 × (x + 4)

or for the slope intercept form we simplify the point-slope form

y + 5 = -3/4 x + -3/4 × 4 = -3/4 x - 3

y = -3/4 x - 8