# Tutor profile: Alexandra A.

## Questions

### Subject: Pre-Algebra

Convert/Change the following equation into slope-intercept form (y=mx+b) and state the slope (m) and y-intercept (b): 4x - 2y = 12.

Step 1: In slope-intercept form y is ALWAYS alone. Our goal is to get y alone in the equation. Start by moving the 4x to the other side. Since we have a positive 4x we are going to do the opposite, and subtract 4x from each side. 4x - 4x will cancel on the left side. 12 - 4x cannot be combined because they are not like terms, so the right side of the equation will stay "12 - 4x" 4x - 2y = 12 -4x -4x -2y = 12 - 4x Step 2: Get the y completely alone. We need to get rid of the "-2." Since the -2 is multiplying the y, we must divide by -2 to get the y alone. Whatever you do to one side you must do to the other. When dividing you must divide EVERYTHING. On the left side, -2/-2 make 1, so we are left with 1y or just y on the left side. On the right side 12/-2 will change to -6 and -4/-2 to get us a positive 2x, so the right side of the equation will change to -6 + 2x. -2y = 12 - 4x /-2 /-2 /-2 y = -6 + 2x Step 3: Identify the slope (m) and y-intercept (b) Now that we have our equation in slope-intercept form: y = -6 + 2x we can find the slope. The slope, m, is always the number attached to x. Slope/m = 2 In a slope-intercept form equation the y-intercept, or b, is always being added or subtracted to the slope. In this equation, y = -6 + 2x, the y-intercept is -6. Y-intercept/b = -6 Step 4: Final Answers Equation: y = -6 + 2x OR y = 2x -6 Slope/m = 2 Y-intercept/b = -6

### Subject: Basic Math

What is 13 $$\div$$ $$\frac{1}{3}$$? Write your answer as a mixed number in simplest form.

Step 1: Make both numbers into a fraction $$\frac{13}{1}$$$$\div$$$$\frac{1}{3}$$ Step 2: Use the "Keep it, switch it, flip it" method $$\frac{13}{1}$$$$\times$$$$\frac{1}{3}$$ Step 3: Multiply numbers straight across $$\frac{13}{1}$$$$\times$$$$\frac{1}{3}$$ = $$\frac{13}{3}$$ Step 4: Simplify result from step 3 by writing it in a mixed number $$\frac{13}{3}$$ = 4$$\frac{1}{3}$$ Step 5: Final Answer 4$$\frac{1}{3}$$

### Subject: Algebra

The area of a rectangular room is 238 square feet. The width is 3 feet less than the length. Find the dimensions of the room.

Define Variables and Write Equation L = Length L - 3 = Width Equation: L (L -3) = 238 Step 1: Distribute L L^2 - 3L = 238 Step 2: Get equation equal to 0 L^2 - 3L - 238 = 0 Step 3: Factor Equation (L-17)(L+14) = 0 Step 4: Set each part of the factor equal to 0 and solve L - 17 = 0 L + 14 = 0 L = 17 L = -14 **The only result for L must be 17. L cannot equal -14 because we are measuring a square, you cannot have a negative measurement** Step 5: Plug in L to both parts of the original equation/defined variables: Length: L Width: L - 3 Length = 17 Width 17-3 Width = 14 Step 6: Final Answer Length: 17 feet Width: 14 feet

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