We can use the point-slope formula to write an equation. However, we must first determine the slope. The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))
Where m is the slope and (color(blue)(x_1, y_1)) and (color(red)(x_2, y_2)) are the two points on the line.
Substituting the values from the points in the problem gives:
m = (color(red)(-7) - color(blue)(3))/(color(red)(0) - color(blue)(-5))
m = (color(red)(-7) - color(blue)(3))/(color(red)(0) + color(blue)(5)) = -10/5 = -2
The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))
Where color(blue)(m) is the slope and color(red)(((x_1, y_1))) is a point the line passes through.
We can substitute the slope we calculated and the first point giving:
(y - color(red)(3)) = color(blue)(-2)(x - color(red)(-5))
(y - color(red)(3)) = color(blue)(-2)(x + color(red)(5))
We can also substitute the slope we calculated and the second point giving:
(y - color(red)(-7)) = color(blue)(-2)(x - color(red)(0))
(y + color(red)(7)) = color(blue)(-2)x
Or, we can solve this equation for y to give an equation in slope-intercept form:
y + color(red)(7) = color(blue)(-2)x
y + color(red)(7) - 7 = color(blue)(-2)x - 7
y + 0 = color(blue)(-2)x - 7
y = color(blue)(-2)x - 7
