Answer:
[tex]y+21 = -4(x-7)[/tex]
Step-by-step explanation:
1) First, find the slope of the line between the two points. Use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of (7, -21) and (-4, 23) into the formula and simplify:
[tex]m = \frac{(23)-(-21)}{(-4)-(7)} \\m = \frac{23+21}{-4-7}\\m = \frac{44}{-11}\\m = -4[/tex]
So, the slope of the line is -4.
2) Now we have all the information we need. To write the equation of the line, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute -4 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (7, -21) into the equation as well. This gives the following answer:
[tex]y+21 = -4(x-7)[/tex]
