First, we need to determine the slope of the line. 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)(1) - color(blue)(8))/(color(red)(0) - color(blue)(-8)) = (color(red)(1) - color(blue)(8))/(color(red)(0) + color(blue)(8)) = -7/8
We can now use the point-slope formula to write and equation for the line running between the two points in the problem. 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.
Substituting the slope we calculated and the values from the first point in the problem gives:
(y - color(red)(8)) = color(blue)(-7/8)(x - color(red)(-8))
(y - color(red)(8)) = color(blue)(-7/8)(x + color(red)(8))
We can also substitute the slope we calculated and the values from the second point in the problem giving:
(y - color(red)(1)) = color(blue)(-7/8)(x - color(red)(0))
(y - color(red)(1)) = color(blue)(-7/8)x
We can also solve this equation for y to put it into slope-intercept form. The slope-intercept form of a linear equation is: y = color(red)(m)x + color(blue)(b)
Where color(red)(m) is the slope and color(blue)(b) is the y-intercept value.
y - color(red)(1) = -7/8x
y - color(red)(1) + 1 = -7/8x + 1
y - 0 = -7/8x + 1
y = color(red)(-7/8)x + color(blue)(1)
