First, we need to determine the slop 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)(3) - color(blue)(6))/(color(red)(-7) - color(blue)(5)) = (-3)/-12 = 1/4
Next we can use the point-slope formula to write and 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)(6)) = color(blue)(1/4)(x - color(red)(5))
We can also substitute the slope we calculated and the values from the second point in the problem giving:
(y - color(red)(3)) = color(blue)(1/4)(x - color(red)(-7))
(y - color(red)(3)) = color(blue)(1/4)(x + color(red)(7))
We can also solve this equation for y to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: v
Where color(red)(m) is the slope and color(blue)(b) is the y-intercept value.
y - color(red)(3) = (color(blue)(1/4) xx x) + (color(blue)(1/4) xx color(red)(7))
y - color(red)(3) = 1/4x + 7/4
y - color(red)(3) + 3 = 1/4x + 7/4 + 3
y = 1/4x + 7/4 + (4/4 xx 3)
y = 1/4x + 7/4 + 12/4
y = color(red)(1/4)x + color(blue)(19/4)
