Linear Equations and Functions

In this video, Michelle guides viewers through solving the first five problems of the 2022 Grade 8 Mathematics Day Exam for New York State. The tutorial covers identifying increasing functions, solving linear equations, calculating the volume of rectangular prisms, determining the equation of a line in slope-intercept form, and using properties of vertical angles to find unknown values. Each problem is explained step-by-step, providing a clear understanding of the mathematical concepts involved.

Which graph represents a function that is increasing?

• A vertical line

• A horizontal line

• A line that increases

• A line that decreases

What is the first step in solving the equation 2.5x + 5 = 7.5x - 0.5?

• Add 5 to both sides

• Distribute 2.5 to x and 5

• Divide both sides by 5

• Subtract 2.5x from both sides

After distributing, what is the equation 2.5x + 5 = 7.5x - 0.5 transformed into?

• 2.5x + 5 = 7.5x + 5

• 2.5x + 5 = 7.5x + 0.5

• 2.5x + 12.5 = 7.5x - 0.5

• 2.5x + 5 = 7.5x - 5

What is the solution to the equation 2.5x + 5 = 7.5x - 0.5?

• x = 1.5

• x = 4.2

• x = 3.5

• x = 2.6

What is the volume of Box A with dimensions 35 cm height, 20 cm length, and 9 cm width?

• 7200 cubic centimeters

• 6300 cubic centimeters

• 4500 cubic centimeters

• 5400 cubic centimeters

What is the volume of Box B with dimensions 25 cm height, 19 cm length, and 6 cm width?

• 2500 cubic centimeters

• 2950 cubic centimeters

• 3150 cubic centimeters

• 2850 cubic centimeters

What is the difference in volume between Box A and Box B?

• 2000 cubic centimeters

• 1650 cubic centimeters

• 1500 cubic centimeters

• 1800 cubic centimeters

What is the slope of the line if it rises 5 units and runs 2 units?

• 2/5

• 5

• 5/2

• 2

What is the y-intercept of a line if the y-value is 4 when the point is on the y-axis?

• 5

• 2

• 3

• 4

What is the equation of the line with a slope of 5/2 and a y-intercept of 4?

• y = 2x + 5

• y = 5x + 2

• y = 2/5x + 4

• y = 5/2x + 4