Note: this answer assumes that it can be written in point-slope form.
Answer:
Equation: [tex]y - 1 = -\frac{4}{5} (x+5)[/tex]
Graph is attached below.
Step-by-step explanation:
1) First, find the slope of the two lines using the slope formula, [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Use the x and y values of the two points given and solve:
[tex]\frac{(-7)-(1)}{(5)-(-5)}\\= \frac{-7-1}{5+5}\\= \frac{-8}{10}\\= \frac{-4}{5}[/tex]
Therefore, the slope is [tex]\frac{-4}{5}[/tex].
2) Next, use the point-slope formula [tex]y-y_1 = m(x-x_1)[/tex] to write the equation. The [tex]m[/tex] represents the slope of the line, so substitute [tex]\frac{-4}{5}[/tex] for
[tex]y - (1) = -\frac{4}{5}(x-(-5)\\y - 1 = -\frac{4}{5} (x+5)[/tex]
Therefore, [tex]y - 1 = -\frac{4}{5} (x+5)[/tex] is the equation of the line.
3) To graph the equation, you can just plot the points (-5,1) and (5,-7) and draw a line with arrows passing through them. After all, you only need two points to graph a line. The graph is attached below.
