Question 1203418
your 3 points are:
a = (-3,0)
b = (-1,-1)
c = (5,-4)


if they are on the same straight line, then they should be able to form an equation with the same slope and same y-interept.


straight line formula is y = mx + b
m is the slope
b is the y-intercept.


you can find the straight line equation from any two of the ponts.
then you can determine if the third point is on the same line by using the equation.


i chose points (-3,0) and (5,-4)
slope is (y2-y1) / (x2-x1)
assigned (-3,0) to (x1,y1)
assigned (5,-4) to (x2,y2)


(y2-y1)/(x2-x1) = (-4-0) / (5--3) = -4/8 = -1/2.


y = mx + b becomes y = -1/2 * x + b


to find the y-intercept, replace x and y with values from one of the points.
i chose (5,-4).
at that point, x = 5 and y = -4
y = -1/2 * x + b becomes -4 = -1/2 * 5 + b
solve for b to get b = -4 + 1/2 * 5 = -4 + 2.5 = -1.5
y-intercept is -1.5 and equation becomes y = -1/2 * x - .5


your third point should be (-1,-1).
to prove that is on the line, replace x in the equation with -1 and solve for y.
you get y = -1/2 * -1 - 1.5 which is equal to 1/2 - 1.5 which is equal to -1.
this means the point (-1,-1) is also on the same line.


here is a graph of the equation y = -1/2 * x - 1.5.
it shows that all 3 points are on the same line.


<img src = "http://theo.x10hosting.com/2023/083001.jpg">