What is the slope-intercept form of the line passing through  (-1, 4)  and  (-4, 1) ?

May 27, 2018

$y = x + 5$

Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-1,4)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 4 , 1\right)$

$m = \frac{1 - 4}{- 4 - \left(- 1\right)} = \frac{- 3}{- 3} = 1$

$y = x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(-4,1)" then}$

$1 = - 4 + b \Rightarrow b = 1 + 4 = 5$

$y = x + 5 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$