Math 8 (Module 4) Understanding Slope and Proportionality

What is the definition of a proportional relationship?

• A relationship defined by a variable that changes independently of the other.

• A relationship where one quantity increases while the other decreases.

• A relationship that has no correlation between the two quantities.

• A relationship where the ratio between two quantities is constant.

How do you calculate the slope of a line given two points?

• slope = (y2 - y1) / (x2 - x1)

• slope = (y2 * y1) / (x2 * x1)

• slope = (y1 + y2) / (x1 + x2)

• slope = (x2 - x1) / (y2 - y1)

If two triangles are similar, how does that relate to their slopes?

• The slopes of corresponding sides are unrelated.

• The slopes of corresponding sides of similar triangles are proportional.

• The slopes of corresponding sides are always equal.

• The slopes of similar triangles are always negative.

What is direct variation and how is it represented mathematically?

• y = kx^2

• y = k/x

• y = k + x

• Direct variation is represented mathematically as y = kx.

Write the slope-intercept form of a line with a slope of 3 and a y-intercept of -2.

• y = -3x - 2

• y = 3x + 2

• y = 3x - 2

• y = 2x - 3

How do you graph a linear equation in slope-intercept form?

• Draw a vertical line at the y-intercept.

• Plot the y-intercept and use the slope to find another point, then draw a line.

• Graph the equation by finding the x-intercept first.

• Use only the slope to draw the line without the y-intercept.

If a line has a slope of 0, what does that tell you about the line?

• The line is vertical.

• The line has a slope of 1.

• The line is curved.

• The line is horizontal.

What is the slope of a line that goes through the points (1, 2) and (3, 6)?

• 4

• 1

• 2

• 3

Explain how to determine if two lines are parallel using their slopes.

• Two lines are parallel if they intersect at a right angle.

• Two lines are parallel if their slopes are equal.

• Two lines are parallel if one slope is negative and the other is positive.

• Two lines are parallel if their slopes are different.

What does it mean for a relationship to be linear?

• A relationship is linear if it can be represented by a straight line, indicating a constant rate of change between the variables.

• A relationship is linear if it involves multiple variables changing at different rates.

• A relationship is linear if it shows no correlation between the variables.

• A relationship is linear if it can be represented by a curved line.