Question

Find the equation of the line that goes through the points (4, –1) and (2, –5).

Answer 1

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-1)}{2-4}\implies \cfrac{-5+1}{-2}\implies \cfrac{-4}{-2}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=2(x-4) \\\\\\ y+1=2x-8\implies y=2x-9$

Answer 2

Answer:

m=2

b=-9

Slope intercept form : y=2x-9

Step-by-step explanation:

The slope intercept form of a line is

$y=mx+b$           .... (1)

where, m is slope and b is y-intercept.

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

where,

$m=\frac{y_2-y_1}{x_2-x_1}$

It is given that the line that goes through the points (4, –1) and (2, –5).

Slope of the line is

$m=\frac{-5-(-1)}{2-4}=2$

The slope of the line is 2.

The line passes through a points (4,-1) with slope 2, so the equation of line is

$y-(-1)=2(x-4)$

$y+1=2x-8$

Subtract 8 from both sides.

$y=2x-8-1$

$y=2x-9$            .... (2)

On comparing (1) and (2) we get

$m=2,b=-9$

Therefore, the y-intercept (b) of the line is -9 and point slope form is y=2x-9.