linear relations

1. Which of the following represents a linear relation? A) y = 2x + 3 B) y = x^2 + 1 C) y = 3sin(x) D) y = 4/x

A) y = 2x + 3

2. What is the slope of the line represented by the equation y = 5x - 2?

The slope is 5.

3. In the equation y = mx + b, what does 'b' represent?

b represents the y-intercept.

4. Given the points (1,2) and (3,6), calculate the slope of the line between these points.

The slope is 2.

5. Write the equation of a line with a slope of 4 and a y-intercept of -3 in the form y = mx + b.

y = 4x - 3.

6. A table shows the following values: x: 2, 4, 6; y: 5, 9, 13. What is the slope of the line represented by this table?

The slope is 2.

7. Create an equation in the form y = mx + b using the table: x: 0, 1, 2, y: 3, 5, 7.

y = 2x + 3.

8. If the y-intercept of a line is (0,4), what is the value of b in the equation y = mx + b?

b = 4.

9. Interpret the slope of the line in the context of this word problem: A cyclist travels 12 miles in 1 hour. What is the slope?

The slope is 12 miles per hour.

10. Given the linear equation y = -3x + 9, what is the y-intercept?

The y-intercept is 9.

11. Graph the linear equation y = 2x - 1. What is the point where the line crosses the y-axis?

The line crosses the y-axis at (0, -1).

12. A store sells notebooks for $2 each. Write an equation to represent the total cost (y) of x notebooks.

y = 2x.

13. From the graph of a linear relation, if the line goes through the points (2, 3) and (4, 7), what is the slope?

The slope is 2.

14. Identify the pattern from the following table: x: 1, 2, 3; y: 2, 4, ?.

The missing y-value is 6.

15. A car rental company charges a flat fee of $50 plus $15 per day. Write the equation for the total cost y of renting for x days.

y = 15x + 50.

16. A linear graph rises from left to right. What can you conclude about the slope?

The slope is positive.

17. If a line has a slope of -4, what can you say about the relationship it represents?

As x increases, y decreases; they are inversely related.

18. A table shows the following: x: 1, 2, 3; y: 4, ?, 12. Find the missing value of y.

The missing value of y is 8.

19. The linear equation y = rac{1}{2}x + 1 represents a relationship. What is the rate of change?

The rate of change is rac{1}{2}.

20. A line on a graph decreases from (3, 5) to (7, 1). Write an equation for this line.

y = -x + 8.