Answer: [tex]y=-2x-3[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form, is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
By definition, parallel lines have the same slope.
Then:
- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-3}{-6-(-7)}=-2[/tex]
- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:
[tex]5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3[/tex]
Then, the equation for the line containing the side opposite the side containing the first two vertices is:
[tex]y=-2x-3[/tex]
