Write an equation in slope-intercept form of the line that passes through the points ( − 1 , 10 ) and ( 6 , − 4 ) .

Answer 1

The slope-intercept form of the equation of a line is : y = mx + b where m is the slope of the line and b is the y-intercept. You can determine the slope of the line using the two points given in the problem as follows:

The slope, m , will be (y₂ - y₁) / (x₂ - x₁).

For this problem, the slope, m, will be (-4 -10) / (6 - (-1)) OR -14/7

Also -14/7 is equivalent to -2 in simplest form. Therefore, the slope of the line is -2

Now to determine the y-intercept, b, use one of the points and the slope as follows (you can select either point ; I will use -1, 10):

y= mx + b

10 = -2 * -1 + b

10 = 2 + b

10 - 2 = 2 + b +-2

8 = b

Therefore, the equation of the line is: y = -2x + 8

You can always verify your equation by substituting the coordinates of one of the given points in the equation:

y = -2x + 8 USE ( 6, -4)

-4 = -2*6 + 8

-4 = -12 + 8