Question

2.A line goes through the points (4, 8) and (-4, 6). (a)What is the slope of the line? Show your work(b)Write the equation of the line in point-slope form. Show your work(c)Write the equation of the line in slope-intercept form. Show your work.

Answer 1

The line passing through two points that are

`(x_1,y_1_{})=(4,8),\text{ }(x_2,y_2)=(-4,6)`

Part (a)

The formula for the slope of a line is given below

`m=(y_2-y_1)/(x_2-x_1)=(6-8)/(-4-4)=(-2)/(-8)=(1)/(4)`

Therefore, the slope of the line is 1/4.

Part (b)

The point-slope form of a line given by the formula

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

Substitute the values and find the equation of the line as follows

`y-4=(1)/(4)(x-8)`

Part (c)

The slope-intercept form of a line has the general form of

`y=mx+c`

Now, manipulate the equation in part (b) to convert it into the above form as follows

`\begin{gathered} y-4=(1)/(4)(x-8) \\ \Rightarrow4y-16=x-8 \\ \Rightarrow4y=x+8 \\ \Rightarrow y=(1)/(4)x+2 \end{gathered}`