Write an equation in slope-intercept form of the line that passes through (6, −1) and (3, −7).

Question

I am not sure how to get the answer. can I please have some help.

Answer 1

You are asked to find the equation of the line that passes through 2 points: (6,-1) and (3,-7).

1st step: Find the slope of the line

slope: m = change in y / change in x

m = (-1 - (-7)) / (6 - 3)

m = (-1 + 7) / (6 - 3)

m = 6 / 3

m = 2

2nd step: Put one of the given points and the slope into the "Point-Slop formula": y - y₁ = m (x - x₁) and simplify to obtain the equation in Slope-Intercept Form

y - (-1) = 2 (x - 6)

y + 1 = 2x -12

y = 2x -12 -1

y = 2x -13

Equation of the line that passes through (6,-1) and (3,-7) in Slope-Intercept Form: y = 2x -13

Note: "Slope-Intercept Form" means that the equation is denoting the Slope (m) and the y-intercept (b):

y = mx + b

Answer 2

You are looking for the equation of a Line (y = mx + c) given 2 points (x1,y1) and (x2,y2). To define y = mx + c, you need the values of m and c.

First find the slope m:

m = change in y / change in x = -7-(-1) / (3-6) = -6/-3 = 2

Now, find the intercept c, by substituting the value of m into y = mx+c with either point:

y1 = m x1 + c ====> c = y1 - m x1 = -1 - 2 (6) = -13

or

y2 = m x2 + c ====> c = y2 - m x2 = -7 - 2 (3) = -13

Now sub both m and c to get your slope-intercept form:

y = m x + c

y = 2 x - 13