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

Feb 24, 2016

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 $\textcolor{b l u e}{\text{ gradient formula }}$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

where$\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2 , y_2 ) " are 2 coord points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(5 , 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , - 2\right)$

hence : $m = \frac{- 2 - 4}{3 - 5} = \frac{- 6}{- 2} = 3$

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

$\Rightarrow y = 3 x - 11 \text{ is the slope-intercept form }$