Answer:
y = -2/7(x) + 3
Step-by-step explanation:
The equation of a line can be stated as y = mx + b, where m is the slope and b is the y-intercept (the value of the function when x = 0). To find the equation of the line, we'll start by finding the slope.
The slope can be expressed as [tex]\frac{y_{2} - y_{1}}{x_{2}-{x_1}}[/tex]
Substituting in our coordinates, we have:
[tex]m = \frac{1 - 5}{7 - (-7)} = \frac{-4}{7 + 7} = \frac{-4}{14}[/tex], which can be simplified to [tex]-\frac{2}{7}[/tex]
Plugging that back into our equation, we have y = [tex]-\frac{2}{7}[/tex]x + b
Now, to find b, we substitute in one of our sets of coordinates. Let's use (-7, 5)
x = -7 and y = 5, which gives us:
[tex]5 = -\frac{2}{7} (-7) + b[/tex]
[tex]-\frac{2}{7} (-7) = 2[/tex], which gives us:
5 = 2 + b
Subtracting 2 from both sides, we get:
3 = b
Plugging that back into our equation, we have [tex]y = -\frac{2}{7} x + 3[/tex]
