Question

1. Line Q goes through (-6,7) and (4,-2). Write the equation of line Q.

Answer 1

First, find the slope of the line using the slope formula:

Provided two points (a,A) and (b,B) on a line, its slope is given by:

`m=(A-B)/(a-b)`

For the points (-6,7) and (4,-2), we have:

`\begin{gathered} m=(7--2)/(-6-4) \\ =(7+2)/(-10) \\ =(9)/(-10) \\ \therefore m=-(9)/(10) \end{gathered}`

The equation of a line in slope-intercept form, of a line with slope m and y-intercept b is:

`y=mx+b`

Substitute m=-9/10 and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):

`\begin{gathered} 7=-(9)/(10)(-6)+b \\ \Rightarrow7=(54)/(10)+b \\ \Rightarrow b=7-(54)/(10) \\ \therefore b=(8)/(5) \end{gathered}`

Substitute b=8/5 and m=-9/10 to find the equation of line Q:

`y=-(9)/(10)x+(8)/(5)`