Answer:
[tex]y=-7x-21[/tex]
Step-by-step explanation:
We have been given two points on a line as [tex](-4,7)[/tex] and [tex](-2,-7)[/tex]. We are asked to find the equation of the line passing through these points.
We will write our equation in slope-intercept form [tex]y=mx+b[/tex], where m represents slope of line and b represents the y-intercept.
Let us find slope of line using our given points as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-7-7}{-2-(-4)}[/tex]
[tex]m=\frac{-14}{-2+4}[/tex]
[tex]m=\frac{-14}{2}[/tex]
[tex]m=-7[/tex]
Now, we will substitute [tex]m=-7[/tex] and coordinates of point [tex](-4,7)[/tex] in slope-intercept form of equation as:
[tex]7=-7(-4)+b[/tex]
[tex]7=28+b[/tex]
[tex]7-28=28-28+b[/tex]
[tex]-21=b[/tex]
Substitute [tex]-21=b[/tex] and [tex]m=-7[/tex] in slope-intercept form of equation:
[tex]y=-7x-21[/tex]
Therefore, our required equation would be [tex]y=-7x-21[/tex].
