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)(0) - color(blue)(-2))/(color(red)(4) - color(blue)(-4)) = (color(red)(0) + color(blue)(2))/(color(red)(4) + color(blue)(4)) = 2/8 = 1/4
We can use the point-slope formula to find an equation for the line. 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)(-2)) = color(blue)(1/4)(x - color(red)(-4))
(y + color(red)(2)) = color(blue)(1/4)(x + color(red)(+4))
We can also substitute the slope we calculated and the values from the second point in the problem giving:
(y - color(red)(0)) = color(blue)(1/4)(x - color(red)(4))
We can solve this for equation for y to put the equation in 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)(0) = (color(blue)(1/4) xx x) - (color(blue)(1/4) xx color(red)(4))
y = 1/4x - color(red)(4)/color(blue)(4)
y = color(red)(1/4)x - color(blue)(1)
