Christopher C.
asked • 01/19/16Rewrite a linear equation in slope-intercept form
y+5 -3 (x+6)
5
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1 Expert Answer
Don L. answered • 01/19/16
Tutor
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Fifteen years teaching and tutoring basic math skills and algebra
Hi Christopher, thanks for clear that up. What is given is a line in point-slope format. To put the line into the slope-intercept form, simply solve for y.
y + 5 = (-3 / 5) * (x + 6)
y + 5 = (-3 * x) / 5 - (18 / 5)
Subtract 5 from both sides:
y = (-3 * x) / 5 - (43 / 5) [-5 is replaced by -25 / 5, which is added to the -18 / 5]
y = -3x / 5 - 43 / 5
You may have to replace -43/5 with a mixed fraction.
Questions?
Christopher C.
Where does -43 come from
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01/19/16
Don L.
tutor
Hi Christopher, good question. When you subtract the 5 from both sides to isolate the y, it becomes -5 on the right side of the equation.
The right side of the equation now has -18 / 5 and -5. In order to combine them, convert the -5 to -25 / 5. Now we have -18 / 5 and -25 / 5. When they are combined it becomes -43 / 5.
Does this help?
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01/19/16
Christopher C.
After using the distributive property i have y+5=-3/5x-18/5
I am lost after that
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01/19/16
Don L.
tutor
Hi Christopher, you have to isolate the y variable. To do that, you need to subtract 5 from both sides.
Starting with:
y + 5 = -3x / 5 - 18 / 5
Subtract 5 from both sides:
y + 5 - 5 = -3x / 5 - 18 / 5 - 5
y = -3x / 5 - 18 / 5 - 5
You need to combine (add together) the -18 / 5 and -5. How can you combine a fraction and a whole number? Answer: by making the whole number into a fraction.
-5 becomes -25 / 5. This gives the same denominator as the term, -18 / 5.
Now add -18 / 5 and -25 / 5, which gives -43 / 5.
Questions?
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01/19/16
Christopher C.
Yes my uncertainty is where -25 comes from because -18 - (-5)=23
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01/19/16
Don L.
tutor
Hi Christopher, when you subtract 5 from both sides, you are left with -5 on the right side of the equation. -5 is a whole number and you need a fraction.
if you have 1, that can be written as 5 / 5. If you have 2, it can be written as 10 / 5. If you have 5, it can be written as 25 / 5. If you have -5, which we do, it can be written as -25 / 5.
You cannot add or subtract a fraction and a whole number. You need to put both numbers in the same terms. Here we have -18 / 5. That is a fraction. We also have -5, that is not a fraction, it is a whole number. You must convert the whole number into a fraction. The whole number, -5, written as a fraction becomes -25 / 5.
Now you have two fractions with the same denominator, which is 5. You can add the numerators, -18 and -25, which becomes -43.
The new fraction is -43 / 5.
Questions?
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01/19/16
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Don L.
01/19/16