Question

Find the slope-intercept form of the line through (−1,3) and (7,−8)

Answer 1

`\sf y =(-11)/(8)x +(13)/(8)`

Explanation:

Slope-intercept form: y = mx + b

Here, m is the slope and b is the y-intercept.

( -1, 3) ; x₁ = -1 & y₁ = 3

(7, -8) ; x₂ = 7 & y₂ = -8

Slope can be obtained by the formula:

`\sf \boxed{\bf Slope = (y_2-y_1)/(x_2-x_1)}`

`\sf =(-8-3)/(7-[-1])\\\\\\=(-8-3)/(7+1)\\\\\\=(-11)/(8)`

Now, we can find the y-intercept,

`\sf y = (-11)/(8)x + b\\\\Substitute \ any \ one \ of \ the \ point \ in \ the \ above \ equation.\\\\\text{Here, we are substituting (-1 ,3)}\\\\3 = (-11)/(8)*(-1) + b\\\\3 = (11)/(8)+b\\\\b = 3 - (11)/(8)\\\\b = (3*8)/(1*8)-(11)/(8)\\\\b= (24-11)/(8)\\\\b= (13)/(8)`

Slope-intercept form:

`\sf y =(-11)/(8)x +(13)/(8)`