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.

Step-by-step 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=(y2-y1)/(x2-x1) \\ \\ =(2-5)/(-5-1) \\ \\ =(-3)/(-6) \\ \\ =(1)/(2) \end{gathered}`

Therefore the equation of line is

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

Here the x-intercept is

`\begin{gathered} 0=(1)/(2)x+(9)/(2) \\ \\ (1)/(2)x+(9)/(2)=0 \\ \\ (1)/(2)x=-(9)/(2) \\ \\ x=-9 \end{gathered}`

And the y-intercept is,

`\begin{gathered} y=0+(9)/(2) \\ \\ y=(9)/(2) \end{gathered}`

Final Answer:

The line equation is :

`y=(1)/(2)x+(9)/(2)`

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

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