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

y = (-1/3)x + 2

Step-by-step explanation:

Equation of line in slope-intercept form is given by

y = mx +c

where m is the slope of line

c is y intercept

Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)

let the equation of required line be y = mx +c

Since points given are  (3,1) and (-6,4)

Then, its slope is

m = 4-1/-6-3 = 3/-9 = -1/3

Thus, slope of line is m = -1/3

lets use m = -1/3 in place of m in equation y = mx +c

y = (-1/3)x + c

Since points   (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.

hence lets plug 3 in place of x and 1 in place of y

1 =  (-1/3)3 + c

=> 1 = -1 + c

=> c = 1 +1 = 2

Thus, intercept is 2.

Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.