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:
[tex]m=\frac{A-B}{a-b}[/tex]For the points (-6,7) and (4,-2), we have:
[tex]\begin{gathered} m=\frac{7--2}{-6-4} \\ =\frac{7+2}{-10} \\ =\frac{9}{-10} \\ \therefore m=-\frac{9}{10} \end{gathered}[/tex]The equation of a line in slope-intercept form, of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]Substitute m=-9/10 and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):
[tex]\begin{gathered} 7=-\frac{9}{10}(-6)+b \\ \Rightarrow7=\frac{54}{10}+b \\ \Rightarrow b=7-\frac{54}{10} \\ \therefore b=\frac{8}{5} \end{gathered}[/tex]Substitute b=8/5 and m=-9/10 to find the equation of line Q:
[tex]y=-\frac{9}{10}x+\frac{8}{5}[/tex]