# Tutor profile: Beverly M.

## Questions

### Subject: Pre-Algebra

What is the slope of the line that contains the points $$(4, 6)$$ and $$(13, -9)$$ ?

To find the slope of a line given two point. We must know the formula for finding the slope when given two points. Formula: when given points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ $$m = \frac{y_{1} - y_{2}}{x_{1}- x_{2}}$$ = slope Next let's plug our points into the equation: $$(4, 6)$$ and $$(13, -9)$$ $$m = \frac{6 - (-9)}{4 -13}$$ $$m =- \frac{15}{9}$$ The slope of the line is -$$\frac{15}{9}$$

### Subject: Basic Math

Sally walked $$½$$ of a mile yesterday and $$¾$$ of a mile today. How many miles has Sally walked?

Set up the expression. We want to know how many total miles Sally walked which requires the use of Addition. Notes for adding fractions. Look at the denominator: If same denominator we can simply add the numerators and simplify. If different denominator we need to find the Least Common Denominator (LCD) Step 1. Setting up our expression $$\frac{1}{2}+\frac{3}{4}=x$$ Step 2: Identify denominator Different denominators Step 3: Find the LCD. Since 2 is a multiple of 4 we know that the LCD is 4. Step 4: Multiply the fraction $$\frac{1}{2}$$ by $$\frac{2}{2} = 1$$ $$\frac{2}{4}+\frac{3}{4}=x$$ *Note: By multiplying by 1 does not change the original equation Step 5: Combine like terms $$\frac{5}{4} = x$$ Solution: Sally walked $$\frac{5}{4}$$ miles.

### Subject: Algebra

Solve for x: $$2x^2+4(x^2 + 3) -2 =22$$

First let us take note of the order of operations: Please (Parentheses) Excuse (Exponents) My (Multiplication) Dear (Division) Aunt (Addition) Sally (Subtraction) *Note that the M and D and A and S are to be solved in the order they are received. Let’s solve: $$2x^2+4(x^2+3)-2=22$$ Step 1: My (Multiplication) Multiply 4 by the expressions inside the parentheses. $$2x^2+4x^2+12-2=22$$ Step 2: Aunt (Addition) Add $$2x^2+4x^2$$ $$6x^2+12-2=22$$ Step 3: Sally (Subtraction) Subtract $$12-2$$ $$6x^2+10=22$$ Step 4: Set the equation equal to zero Subtract $$22$$ from both sides $$6x^2+10-22=0$$ Step 5: Sally (Subtraction) Subtract $$10-22$$ $$6x^2-12=0$$ Step 6: Solve for $$x$$ Add $$12$$ to both sides $$6x^2=12$$ Step 7: Solve for $$x$$ ctd. Divide by $$6$$ on both sides $$x^2=2$$ Step 8: Solve for $$x$$ ctd. Take the Square Root of both sides x=$$\sqrt{2}$$ and $$-\sqrt{2}$$ Step 9: Check your answer by plugging in $$x$$ $$2x^2+4(x^2+3)-2=22$$ $$2[(\sqrt{2})^2+4((\sqrt{2})^2+3)-2=22$$ $$2(2)+4(2+3)-2=22$$ $$4+4(5)-2=22$$ $$4+20-2=22$$ $$24-2=22$$ $$22=22$$ *Note: A negative number squared is a positive number thus same answer for $$-\sqrt{2}$$