We can use the point-slope formula to find a line passing through these two points.
First, however, we must use the two points to determine the slope.
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 given in the problem produces:
m = (color(red)(3) - color(blue)(-2))/(color(red)(4) - color(blue)(9))
m = (color(red)(3) + color(blue)(2))/(color(red)(4) - color(blue)(9))
m = 5/-5 = -1
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.
We can now substitute the first point from the problem and the slope we calculated to obtain an equation:
(y - color(red)(-2)) = color(blue)(-1)(x - color(red)(9))
(y + color(red)(2)) = color(blue)(-1)(x - color(red)(9))
We also substitute the second point from the problem and the slope we calculated to obtain another equation:
(y - color(red)(3)) = color(blue)(-1)(x - color(red)(4))
We can solve this problem for y to obtain the equation in the familiar slope-intercept form:
y - color(red)(3) = (color(blue)(-1) xx x) - (color(blue)(-1) xx color(red)(4))
y - color(red)(3) = -1x + 4
y - color(red)(3) + 3 = -1x + 4 + 3
y - 0 = -1x + 7
y = -1x + 7 or y = -x + 7
