First, we need to determine the slope of the line running through the two points. 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)(385) - color(blue)(169))/(color(red)(10) - color(blue)(4)) = 216/6 = 36
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.
We can substitute the slope we calculated for m and the values from one of the points can be substituted for x and y and we can solve for b:
385 = (color(red)(36) * 10) + color(blue)(b)
385 = 360 + color(blue)(b)
-color(red)(360) + 385 = -color(red)(360) + 360 + color(blue)(b)
25 = 0 + color(blue)(b)
25 = color(blue)(b)
color(blue)(b) = 25
We can now substitute the slope and value for b we calculated into the formula to obtain the formula for the line:
y = color(red)(36)x + color(blue)(25)
