Question

What is an equation of the line that passes through the points (-2, -5)and (-1, 1)?

Answer 1

Answer: y = 6x + 7

Step-by-step explanation:

We can use slope formula to find the slope of a line that passes through two points (x₁ , y₁) and (x₂ , y₂)

m = ∆y/∆x = y₂-y₁/x₂-x₁

Given points are: P(x₁ , y₁) = (-2, -5) and Q(x₂ , y₂) = (-1, 1)

Substituting these two known points in the slope formula, we have:

m = (1-(-5))/(-1-(-2)) = 1+5/-1+2 = 6/1 = 6  

Now we can use the point-slope formula to write the equation of a line given a point on the line and the slope of the line:

m = 6 , given point P(x₁,y₁) = (-2, -5)

Formula = (y-y₁) = m(x-x₁)

(y-(-5)) = 6(x-(-2))

y+5 = 6x + 12

y = 6x + 12 -5

y = 6x + 7

Answer: y = 6x + 7

Spymore

Answer 2

First find the slope(m)



Slope= y2-y1/x2-x1= (1-(-5))/(-1-(-2))= 6/1 = 6

Then find the y intercept (move up six and right one from (-1, 1) to get (0, 7)

The y-intercept is y=7

Now make the equation

Y= slope(x) + y-intercept

Y=6x+7