Algebra 1 Math Prep

Find the slope of the line.

• -5/4

• 5/4

• -4/5

• 4/5

Answer explanation

To find the slope of the line, use the formula (y2 - y1) / (x2 - x1). After calculating with the given points, the slope is -5/4, which matches the correct answer.

Tags

CCSS.8.EE.B.5

Elijah is organizing a charity event and needs to create gift bags. He has 15x³⁰ candies and 25x²¹ chocolates. What is the greatest common factor of candies and chocolates that Elijah can use to ensure each gift bag has the same number of candies and chocolates?

• 5x²¹

• 15x²¹

• 5x³⁰

• 15x³⁰

Answer explanation

To find the GCF of 15x^30 and 25x^21, we take the GCF of the coefficients (5) and the lowest power of x (x^21). Thus, the GCF is 5x^21.

Hannah is calculating the value of an expression for her math homework. She needs to find the result of (-4r³s⁵)⁰ (3b⁴c²d)

• 1

• -12b⁴c²d

• 3b⁴c²d

• 0

Answer explanation

Any expression raised to the power of 0 equals 1, so (-4r³s⁵)⁰ simplifies to 1. Therefore, the expression evaluates to 1 * (3b⁴c²d) = 3b⁴c²d.

Tags

CCSS.HSA.APR.A.1

Aria is designing a ramp for a skateboard park. She needs to write the equation in point-slope form of the line that represents the ramp, which passes through a point at (4, -7) and has a slope of m = -1/4.

• y +7 = -1/4(x - 4)

• y - 4 = -1/4(x + 7)

• y+ 7 = 4(x - 4)

• y - 7 = -1/4(x - 4)

Answer explanation

The point-slope form is given by y - y1 = m(x - x1). Here, (x1, y1) = (4, -7) and m = -1/4. Substituting these values gives y + 7 = -1/4(x - 4), which matches the correct answer.

Find the slope of the line that passes through 
(17, 2) and (17, -3)

• 0

• undefined

• 5

• -5

Answer explanation

The slope of a line is calculated as (y2 - y1) / (x2 - x1). Here, both points have the same x-coordinate (17), leading to a division by zero. Therefore, the slope is undefined.

Tags

CCSS.8.EE.B.5

Find the slope from the table:

• -2/5

• 5/-2

• 5/2

• 2/5

Answer explanation

To find the slope from the table, use the formula (change in y) / (change in x). The correct calculation yields a slope of 5/-2, which represents the rate of change between the given points.

Tags

CCSS.8.EE.B.5

Dev keeps a record in graph form of how far his car travels and the number of gallons of gasoline it uses.
What is the slope of the graph?

• 64

• 128

• 32

• 16

Answer explanation

The slope of the graph represents the car's fuel efficiency, calculated as miles per gallon. If Dev's car travels 32 miles per gallon, the slope is 32, indicating it uses 1 gallon of gas for every 32 miles traveled.

Tags

CCSS.8.EE.B.5

Graph. y = 2/3x - 3

• a

• b

• c

• d

Answer explanation

The equation y = 2/3x - 3 represents a linear function with a slope of 2/3 and a y-intercept of -3. The correct graph choice is 'a', which accurately depicts this line.

Abigail is designing a rectangular garden and wants to create a walkway around it. The area of the garden is represented by x² - 25 square meters. What are the dimensions of the garden?

• ( x + 5 ) ( x - 5 )

• ( x - 5 ) ( x - 5 )

• ( x + 5 ) ( x + 5 )

• Unfactorable

Answer explanation

The expression x² - 25 is a difference of squares, which factors as (x + 5)(x - 5). This is the correct choice, as it represents the two binomials that multiply to give the original expression.

Tags

CCSS.HSA-REI.B.4B

David is trying to find two numbers whose product is 6 and sum is 5. What are the numbers?

• (x - 3) (x - 2)

• (x + 3) (x - 2)

• (x + 3) (x + 2)

• (x + 2) (x - 3)

Answer explanation

To factor x² + 5x + 6, we look for two numbers that multiply to 6 and add to 5. The numbers 2 and 3 fit, leading to (x + 2)(x + 3) as the correct factorization.