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)(5) - color(blue)(1))/(color(red)(9) - color(blue)(3)) = 4/6 = 2/3
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 first point from the problem gives:
(y - color(red)(1)) = color(blue)(2/3)(x - color(red)(3))
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. Solving for y gives:
y - color(red)(1) = (color(blue)(2/3) xx x) - (color(blue)(2/3) xx color(red)(3))
y - color(red)(1) = 2/3x - (color(blue)(2/cancel(3)) xx cancel(color(red)(3)))
y - color(red)(1) = 2/3x - 2
y - color(red)(1) + 1 = 2/3x - 2 + 1
y - 0 = 2/3x - 1
y = color(red)(2/3)x - color(blue)(1)
