Question

What is the slope-intercept form of the line passing through `(5, 4)` and `(3, -2)`?

Answer 1

y = 3x - 11

Explanation:

The slope-intercept form of a straight line is y = mx + c , where m represents the gradient (slope) and c, the y-intercept.

To find m , use the `color(blue)" gradient formula "`

`m = (y_2 - y_1)/(x_2 - x_1)`

where`(x_1 , y_1 ) " and " (x_2 , y_2 ) " are 2 coord points "`

let `(x_1,y_1) = (5,4) " and " (x_2,y_2) = (3,-2)`

hence : `m = (-2 - 4)/(3 - 5 ) = (-6)/(-2) = 3`

equation is y = 3x + c and to find c , use one of the given points on the line , say (5 , 4 ).

ie 4 = 3(5) + c → c = 4 - 15 = -11

`rArr y = 3x - 11 " is the slope-intercept form "`