First, we need 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 in the problem gives:
m = (color(red)(0) - color(blue)(10))/(color(red)(9) - color(blue)(-17)) = (color(red)(0) - color(blue)(10))/(color(red)(9) + color(blue)(17)) = -10/26 = -5/13
Now, we can use the point-slope formula to find an 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)(10)) = color(blue)(-5/13)(x - color(red)(-17))
(y - color(red)(10)) = color(blue)(-5/13)(x + color(red)(17))
Or, we can substitute the slope we calculated and the second point from the problem giving:
(y - color(red)(0)) = color(blue)(-5/13)(x - color(red)(9))
y = color(blue)(-5/13)(x - color(red)(9))
Or, we can expand this 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(blue)(-5/13) xx x) - (color(blue)(-5/13) xx color(red)(9))
y = color(red)(-5/13)x + color(blue)(45/13)
Three possible solutions are:
(y - color(red)(10)) = color(blue)(-5/13)(x + color(red)(17))
y = color(blue)(-5/13)(x - color(red)(9))
y = color(red)(-5/13)x + color(blue)(45/13)
