Tutor profile: Danita H.

Find the x- and y-intercepts of the graph of 5x + 4y = 10.

The x-intercept is where the graph crosses the x-axis. At any point on the x-axis, the y-value is always 0. So, to find the x-intercept, we will plug 0 in for y: 5x + 4(0) = 10 (simplify) 5x + 0 = 10 (simplify) 5x = 10 (divide both sides by 5) x = 2 The x-intercept has an x-value of 2 and a y-value of 0. Therefore, our x-intercept is the point (2, 0). The y-intercept is where the graph crosses the y-axis. At any point on the y-axis, the x-value is always 0. So, to find the y-intercept, we will plug in 0 for x: 5(0) + 4y = 10 (simplify) 0 + 4y = 10 (simplify) 4y = 10 (divide both sides by 4) y = 2.5 The y-intercept has a y-value of 2.5 and an x-value of 0. Therefore, our y-intercept is the point (0, 2.5)

\triangle(ABC) ~ \triangle(DEF) If AB = 4, DE = 10, and BC = 6, solve for EF.

When triangles are similar, their corresponding side lengths are proportional. The similarity statement tells us the parts of the triangle that get "matched up" by following the order they are written. From our given statement we know that AB/DE = BC/EF = AC/DF Substituting our given values in for AB, DE, and BC we get 4/10 = 6/EF When cross multiplying you would get 4*EF = 60. Divide both sides by 4 to get EF = 15.

Find the solution to the system of equations: y = 3x + 5 2x + 4y = 34

There are three common methods to solving a system of equations. 1. Graphing 2. Substitution 3. Elimination When solving a system of equations, you are looking for the ordered pair that satisfies both equations, or where the lines would cross when graphed. In this case, I would recommend using substitution because the first equation is already solved for y. Since y is equal to 3x + 5, then 3x + 5 can replace y in the other equation. This would look like: 2x + 4(3x + 5) = 34 First, distribute the 4: 2x + 12x + 20 = 34 Then combine like terms: 14x + 20 = 34 Subtract 20 from both sides of the equation: 14x = 14 Divide both sides by 14: x = 1 The x-value of our solution is 1. To find the y-value, substitute 1 in for x in one of the given equations: y = 3(1) + 5 = 8. The y-value is 8. Write your answer as the ordered pair (1, 8).