First, we need to determine the slope of the line. The formula for find the slope of a line is:
m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))
Where (color(blue)(x_1), color(blue)(y_1)) and (color(red)(x_2), color(red)(y_2)) are two points on the line.
Substituting the values from the points in the problem gives:
m = (color(red)(4) - color(blue)(0))/(color(red)(4) - color(blue)(-12)) = (color(red)(4) - color(blue)(0))/(color(red)(4) + color(blue)(12)) = 4/16 = 1/4
Now, we can use the point-slope formula to write and equation for the line. The point-slope form of a linear equation is: (y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))
Where (color(blue)(x_1), color(blue)(y_1)) is a point on the line and color(red)(m) is the slope.
Substituting the slope we calculated and the values from the first point in the problem gives:
(y - color(blue)(0)) = color(red)(1/4)(x - color(blue)(-12))
y = color(red)(1/4)(x + color(blue)(12))
We can modify this result 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)(1/4)(x + color(blue)(12))
y = (color(red)(1/4) xx x) + (color(red)(1/4) xx color(blue)(12))
y = color(red)(1/4)x + color(blue)(12)/(color(red)(4)
y = color(red)(1/4)x + color(blue)(3)
