A line contains the points (3,1) and (−6,4). A line contains the points (3,1) and (−6,4). What is the equation for this line in slop-intercept form? What is the equation for this line in slop-intercept form?

Step-by-step explanation:

The equation of  a line in slope-intercept form is expressed as y = mx+c

m is the slope of the line

c is the intercept

m = Δy/Δx = y₂-y₁/x₂-x₁

Given the points on a line to be  (3,1) and (−6,4);

x₁ = 3, y₁ = 1, x₂ = -6 and y₂ = 4

m = 4-1/-6-3

m = 3/-9

m = -1/3

To get the intercept c, we will substitute any of the points given and the value of the slope into the equation y = mx+c. Using the point (3, 1) and m = -1/3

1 = -1/3(3)+c

1 = -1+c

c  = 1+1

c =2

Substituting m = -1/3 and c = 2 into the sllpe intercept form of the equation will give;

y = -1/3 x + 2

Hence the  equation for the line in slope-intercept form is y = -1/3 x + 2