What is the equation of the line that passes through (1,5) and (-2,14) in slope intercept form?

Mar 25, 2018

$y = - 3 x + 8$

Explanation:

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

•color(white)(x)y=mx+b

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(1,5)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , 14\right)$

$\Rightarrow m = \frac{14 - 5}{- 2 - 1} = \frac{9}{- 3} = - 3$

$\Rightarrow y = - 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(1,5)" then}$

$5 = - 3 + b \Rightarrow b = 5 + 3 = 8$

$\Rightarrow y = - 3 x + 8 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

Mar 25, 2018

The reqd. equn. of the line is

$3 x + y = 8$ or $y = - 3 x + 8$

Explanation:

If $A \left({x}_{1} , {y}_{1}\right) \mathmr{and} B \left({x}_{2} , {y}_{2}\right)$,then equation of the line:

color(red)((x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1).

We have,

$A \left(1 , 5\right) \mathmr{and} B \left(- 2 , 14\right)$

So,

$\frac{x - 1}{- 2 - 1} = \frac{y - 5}{14 - 5}$.

$\implies \frac{x - 1}{-} 3 = \frac{y - 5}{9}$

$\implies 9 x - 9 = - 3 y + 15$

$\implies 9 x + 3 y = 15 + 9$

$\implies 9 x + 3 y = 24$

$\implies 3 x + y = 8$ or $y = - 3 x + 8$
graph{3x+y=8 [-20, 20, -10, 10]}