Question

Graph and find the equation of the line going through points (1,5) and (-5,2). Then state your x- and y-intercepts, if any

Answer 1

Given:

The line passing through the points (1,5) and (-5,2).

$\begin{gathered} (x1,y1)=(1,5) \\ (x2,y2)=(-5,2) \end{gathered}$

Required:

To find the equation of line, x- and y-intercepts.

Explanation:

The general form of line equation is

$y-y1=m(x-x1)$

Here

$y-5=m(x-1)$

Where m is the slope.

$\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ =\frac{2-5}{-5-1} \\ \\ =\frac{-3}{-6} \\ \\ =\frac{1}{2} \end{gathered}$

Therefore the equation of line is

$\begin{gathered} y-5=\frac{1}{2}(x-1) \\ \\ y=\frac{1}{2}x-\frac{1}{2}+5 \\ \\ y=\frac{1}{2}x+\frac{9}{2} \end{gathered}$

Here the x-intercept is

$\begin{gathered} 0=\frac{1}{2}x+\frac{9}{2} \\ \\ \frac{1}{2}x+\frac{9}{2}=0 \\ \\ \frac{1}{2}x=-\frac{9}{2} \\ \\ x=-9 \end{gathered}$

And the y-intercept is,

$\begin{gathered} y=0+\frac{9}{2} \\ \\ y=\frac{9}{2} \end{gathered}$

Final Answer:

The line equation is :

$y=\frac{1}{2}x+\frac{9}{2}$

The x-intercept is :( -9,0)

The y-intercept is : (0,9/2)