he point-slope formula can be used to find the equation. First we must 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)(4) - color(blue)(-4))/(color(red)(2) - color(blue)(-2))
m = (color(red)(4) + color(blue)(4))/(color(red)(2) + color(blue)(2)) = 8/4 = 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.
Substituting the slope we calculated and the first point gives:
(y - color(red)(-4)) = color(blue)(2)(x - color(red)(-2))
(y + color(red)(4)) = color(blue)(2)(x + color(red)(2))
We can also substitute the slope we calculated and the second point giving:
(y - color(red)(4)) = color(blue)(2)(x - color(red)(2))
We can also solve this equation for y to put the equation in the familiar 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)(4) = (color(blue)(2) xx x) - (color(blue)(2) xx color(red)(2))
y - color(red)(4) = 2x - 4
y - color(red)(4) + 4 = 2x - 4 + 4
y - 0 = 2x - 0
y = 2x
