SOLUTION: Thank you in advance for your help with problem. I need to find 3 coordinates of 3 other points with this info. (5,-1) and the slope of m=-2/3. Thank you so much.

Question 151489This question is from textbook college algebra
: Thank you in advance for your help with problem. I need to find 3 coordinates of 3 other points with this info. (5,-1) and the slope of m=-2/3. Thank you so much. This question is from textbook college algebra

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
I need to find 3 coordinates of 3 other points with this info. (5,-1) and the slope of m=-2/3.
.
Remember the "slope-intercept" form of a line is:
y = mx + b
where
m is the slope
b is the y-intercept at (0,b)
x is the x-coordinate
y is the y-coordinate
.
For your problem, they give you:
a point on the line at (5,-1)
and, the slope of -2/3
.
Strategy is the following:
1. find the equation of the line given the two pieces of info above
2. then, find three additional points on that line from the equation
.
#1: plug in what we know into the "slope-intercept" form and solve for b:
y = mx + b
-1 = (-2/3)(5) + b
-1 = (-10/3) + b
-3 = -10 + 3b
7 = 3b
7/3 = b
.
Now, we know the equation of the line is:
y = (-2/3)x + (7/3)
.
#2: find three other points on that line
How about if we pick the three points at:
x=0
x=1
x=3
.
plug each into our equation and solve for y:
when x=0
y = (-2/3)x + (7/3)
y = (-2/3)0 + (7/3)
y = 7/3
point 1: (0, 7/3)
.
when x=1
y = (-2/3)1 + (7/3)
y = (-2/3) + (7/3)
y = 5/3
point 2: (1, 5/3)
.
when x=3
y = (-2/3)3 + (7/3)
y = -2 + 7/3
y = -6/3 + 7/3
y = 1/3
point 3: (3, 1/3)

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