Question

What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?

A. y+3=4(x+1)

B. y−1=4(x−3)

C. y+1=4(x+3)

D. y−3=4(x−1)

Answer 1

A. y+3=4(x+1)

Explanation:

Lets find an equation having the form y=mx+b, where m is the slope and b the y-intercept. We are given the slope, so let's add that first:

y = 4x + b

That was easy. No how can we find the value for b? We are given a point that the line passes through: (-1,-3). If the line gors through this point, then it must be a valid solution to the equation. Let's use that point in the equation and solve for b:

y = 4x + b

-3 = 4*(-1) + b for point (-1,-3)

-3 = -4 + b

b = 1

The equation becomes y = 4x + 1

Put this into point slope form:

y = 4x + 1

y+3 = 4x + 1 + 3

y+3 = 4x + 4

y+3 = 4(x + 1)

See the attached graph.