Answers:
- First box = 1
- Second box = -5
- Third box = -15
This forms the equation 1x-5y = -15, which is the same as x-5y = -15
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Explanation:
Let's find the slope. I'll pick the first two rows to form the two points needed
(x1,y1) = (0,3)
(x2,y2) = (10,5)
These are then plugged into the slope formula.
m = slope
m = (y2-y1)/(x2-x1)
m = (5-3)/(10-0)
m = 2/10
m = 1/5
m = 0.2
The y intercept is b = 3 since this is the y value when x = 0.
With m = 0.2 and b = 3, we go from y = mx+b to y = 0.2x+3
Let's multiply both sides by 5 to turn that decimal value into a whole number. I'm picking 5 since 0.2 = 1/5
So we get
y = 0.2x+3
5y = 5*(0.2x+3)
5y = 5*0.2x+5*3
5y = x+15
Now let's get x and y together, but move that 15 to its own side
5y = x+15
x+15 = 5y
x = 5y-15
x-5y = -15
This is one way to write the equation in standard form.
Standard form is Ax+By = C, where A,B,C are integers. Some math textbooks insist that A > 0. In this case, A = 1, B = -5, and C = -15.
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As a way to check, we can plug in (x,y) = (15,6) from the third row of the table to see that..
x-5y = -15
15-5(6) = -15
15 - 30 = -15
-15 = -15
This verifies the third row. I'll let you check the first two rows of the table to fully confirm this equation works.
