1 gallon = $3 so the ratio would be 1:3 where 1 would represent the gallon and 3 the price
Mistake in Line 2 : Was in the determining the values for a ,b,c
Mistake in Line 4 : Not taking the square roots of both sides.
Step-by-step explanation:

First Mistake : Line 2

Second Mistake : Line 4

Correct Solution :


Point-slope form is written as : y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point.
The slope (m) is found by the change in Y over the change in X
Slope = (y2 - y1) / (x2 - x1)
You can use either given point for x1 and y1 so you would calculate the slope and replace m with the slope, then replace x1 and y1 in the equation with their value.
We have y - 2 = m(x + 5), where m = (-1 - 2)/(10 + 5) = -3/15 = -1/5;
Then y - 2 = (-1/5)(x + 5);
5y - 10 = (-1)(x + 5);
5y - 10 = -x - 5;
x + 5y - 5 = 0 is the equation of the line.
Answer:
8. Identify the common denominator; express each fraction using that denominator; combine the numerators of those rewritten fractions and express the result over the common denominator. Factor out any common factors from numerator and denominator in your result. (It's exactly the same set of instructions that apply for completely numerical fractions.)
9. As with numerical fractions, multiply the numerator by the inverse of the denominator; cancel common factors from numerator and denominator.
10. The method often recommended is to multiply the equation by a common denominator to eliminate the fractions. Then solve in the usual way. Check all answers. If one of the answers makes your multiplier (common denominator) be zero, it is extraneous. (10a cannot have extraneous solutions; 10b might)
Step-by-step explanation:
For a couple of these, it is helpful to remember that (a-b) = -(b-a).
<h3>8d.</h3>

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<h3>9b.</h3>

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<h3>10b.</h3>

Neither solution makes any denominator be zero, so both are good solutions.