Canada Grade 8 Math Understand relations and representations

Answer explanation

The slope of a line in the equation y = mx + b is represented by the coefficient of x. Here, m = -3, so the slope is -3.

• A line passing through points (0, -1) and (2, 0)

• A line passing through points (0, 1) and (2, 2)

• A line passing through points (0, -1) and (2, 1)

• A line passing through points (0, 0) and (2, 1)

Answer explanation

The equation y = (1/2)x - 1 has a y-intercept at (0, -1) and a slope of 1/2. This means for every 2 units increase in x, y increases by 1. The line passes through (0, -1) and (2, 1), making this the correct choice.

Answer explanation

To find the equation, calculate the slope (m) using points (0,2) and (1,5): m = (5-2)/(1-0) = 3. Using point (0,2) to find the y-intercept (b): 2 = 3(0) + b, so b = 2. The equation is y = 3x + 2.

Which of the following is a linear relation?

Answer explanation

The equation y = 2x + 5 is a linear relation because it can be expressed in the form y = mx + b, where m and b are constants. The other options involve quadratic, square root, and reciprocal functions, which are not linear.

Answer explanation

The y-intercept of a line is the value of y when x = 0. In the equation y = 4x - 7, substituting x = 0 gives y = -7. Therefore, the y-intercept is -7.

Answer explanation

Lines that are parallel have the same slope. The slope of the given line, y = -2x + 3, is -2. The equation y = -2x - 4 also has a slope of -2, making it parallel. The other options have different slopes.

If the graph of a relation passes through the points (1, 2) and (3, 6), what is the slope of the line?

Answer explanation

To find the slope (m) between two points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (6 - 2) / (3 - 1) = 4 / 2 = 2. Thus, the slope is 2.

Which of the following tables represents a non-linear relation?

Answer explanation

The second table shows a non-linear relation because the values of y are the squares of x (1, 4, 9), indicating a quadratic relationship, while the other tables represent linear relationships.

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

Answer explanation

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Here, the slope is 5 and the y-intercept is -2, giving us y = 5x - 2.

Which of the following graphs represents a direct variation?

• A line passing through (0, 2) with a positive slope

• A line passing through (0, 0) with a positive slope

• A line passing through (0, -2) with a negative slope

• A line passing through (0, 0) with a negative slope

Answer explanation

A direct variation is represented by a line that passes through the origin (0, 0). The correct choice is the line passing through (0, 0) with a positive slope, indicating a direct proportional relationship.