Understanding Slopes and Intercepts

The video tutorial covers practice problems from lesson 13, focusing on solving linear equations and graphing their solutions. It includes solving equations with specific values for x and y, graphing the results, and verifying them using slopes and y-intercepts. The tutorial also involves matching equations to their respective graphs and stories, determining if points lie on the same line, and calculating coordinates for given points.

What is the slope of the equation y = 6x + 8?

• 2/3

• 1/2

• 6

• 8

If x = -3, what is the y-coordinate for the equation y = 6x + 8?

• -10

• 18

• 10

• -18

In a proportional relationship, what is the y-intercept?

• Undefined

• Depends on the slope

• 1

• 0

How do you solve for x in the equation 2 = 3/4x - 2.5?

• Add 2.5 to both sides and multiply by 4/3

• Subtract 2.5 from both sides and multiply by 4/3

• Subtract 2.5 from both sides and multiply by 3/4

• Add 2.5 to both sides and multiply by 3/4

What is the equivalent fraction for the decimal 1.5?

• 1/3

• 5/3

• 2/3

• 3/2

Which of the following equations has a negative slope?

• y = 3x - 2

• y = -x + 5

• y = 2x + 3

• y = 0.5x + 1

In the context of a kitten's weight over time, which graph characteristic is most appropriate?

• Starts below zero and decreases

• Starts at zero and remains constant

• Starts at zero and decreases

• Starts above zero and increases

What does the x-intercept of a line represent?

• The point where the line crosses the y-axis

• The point where the line crosses the x-axis

• The slope of the line

• The midpoint of the line

If a line has a slope of 2, what does this indicate about its steepness?

• The line falls 2 units for every 1 unit it moves horizontally

• The line is vertical

• The line is horizontal

• The line rises 2 units for every 1 unit it moves horizontally

How can you determine if three points lie on the same line using an equation?

• Verify if substituting the x-coordinates into the equation gives the corresponding y-coordinates

• See if the points form a triangle

• Check if the x-coordinates are all even

• Ensure the y-coordinates are all positive