Question

Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)

A. y = 1/2x + 1
B. y = x +1
C. y = 1/2x - 1
D. y = x -1

i already know the answer is B but how do you solve questions like these?

Answer 1

When you are given two points on a line, you can use them to find the gradient of the line.
Gradient = rise/run
Say you are given two points (a,b) and (c,d)
Gradient = (d-b)/(c-a)
In the case of your question,
Gradient
= [(-3) - (-1)] ÷ [(-4) - (-2)]
= -2 ÷ -2
= 1
From there, you can sub the gradient and one of the points into the gradient-intercept form of a line to get:
y - (-1) = 1(x - (-2))
y + 1 = x + 2
y = x + 1