Answer:
- x-intercept: (-1.375, 0)
- y-intercept: (0, 2.2)
Explanation:
Each intercept is found by setting the other variable to zero and solving.
x-intercept
Set y=0 and solve:
8x -5·0 = -11
8x = -11 . . . . simplify
x = -11/8 = -1 3/8 = -1.375 . . . . . . divide by 8
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y-intercept
Set x=0 and solve:
8·0 -5y = -11
-5y = -11 . . . . . . simplify
y = -11/-5 = 11/5 = 2 1/5 = 2.2 . . . . . divide by the coefficient of y
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The intercepts are ...
x-intercept: (-1.375, 0)
y-intercept: (0, 2.2)
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Additional comments
When you write the intercept as an ordered pair, the variable that is set to zero will be 0 in the ordered pair. That is, the x-intercept will have y=0, and vice versa.
After you have done a few of these, you see that the intercepts of ...
ax +by = c
are ...
x-intercept = c/a . . . (c/a, 0) as an ordered pair
y-intercept = c/b . . . (0, c/b) as an ordered pair
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Solving any sort of equation has one rule: whatever operation you perform on one side of the equation must also be performed on the other side. Here, we use the wording "divide by 8" to mean "divide both sides of the equation by 8".
Simplification requires an understanding of several other properties of numbers:
a - a = 0
a + 0 = a
a/a = 1
1·a = a