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2 answers:
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Answer:
Step-by-step explanation:
The given line is defined by: , where we see that the slope is 5 and the y-intercept 1.
In order to find a line perpendicular to the given one, we need it to have a slope that is the "opposite of the reciprocal" of the given slope.
"Opposite" means it would have its sign inverted (in our case from positive to negative); and "reciprocal means that instead of 5, it would be its reciprocal: .
We can write this new line with such slope, and try to find its y-intercept (b) by using the given condition that requires it to go through the point (-5,-4) on he plane:
we require then that when , the value of
.
Therefore:
Then our final answer is that the new line should have the form:
Given the equation:
(a) You can identify that the student applied the Subtraction Property of Equality by subtraction 3 from both sides of the equation:
However, the student made a mistake when adding the numbers on the right side.
Since you have two numbers with the same sign on the right side of the equation, you must add them, not subtract them and use the same sign in the result. Then, the steps to add them are:
- Add their Absolute values (their values without the negative sign).
- Write the sum with the negative sign.
Then:
(b) The correct procedure is:
1. Apply the Subtraction Property of Equality by subtracting 3 from both sides (as you did in the previous part):
2. Apply the Multiplication Property of Equality by multiplying both sides of the equation by 6:
Hence, the answers are:
(a) The student made a mistake by adding the numbers -18 and -3:
(b) The value of "x" should be: