1.
Determine the slope of the line.
Correct Answer
C. 4/3
Explanation
The slope of a line can be determined by comparing the change in the y-coordinate to the change in the x-coordinate between any two points on the line. In this case, the slope is 4/3 because for every 4 units that the y-coordinate increases, the x-coordinate increases by 3 units.
2.
Identify the x-intercept of the line.
Correct Answer
B. (-2, 0)
Explanation
The x-intercept of a line is the point where the line intersects the x-axis. In this case, the x-intercept is the point (-2, 0) because it is the only point given where the y-coordinate is 0, indicating that the line crosses the x-axis at that point.
3.
Identify the y-intercept.
Correct Answer
D. (0, 2)
Explanation
The y-intercept is the point where the graph of a function intersects the y-axis. In this question, the point (0, 2) is the only option that lies on the y-axis. Therefore, it represents the y-intercept of the function.
4.
Identify the x-intercept in the table.
Correct Answer
B. (-0.5, 0)
Explanation
The x-intercept is the point where the graph of a function crosses the x-axis. In this table, the x-intercept occurs when the y-coordinate is 0. The only point with a y-coordinate of 0 is (-0.5, 0), so it is the x-intercept.
5.
Determine the y-intercept from the table.
Correct Answer
D. (0, 3)
Explanation
The y-intercept is the point where the graph of a function intersects the y-axis. In other words, it is the value of y when x is equal to 0. Looking at the table, we can see that when x is 0, y is 3. Therefore, the y-intercept is (0, 3).
6.
The y-intercept of the function y=3x + 4 is the point (0, 4).
Correct Answer
A. True
Explanation
The y-intercept of a function is the point where the graph of the function intersects the y-axis. In the given function y=3x + 4, when x is 0, the equation becomes y=3(0) + 4, which simplifies to y=4. Therefore, the y-intercept of the function is the point (0, 4).
7.
What is the slope and y-intercept of the function y= -5x - 2?
Correct Answer
B. M = -5 and b = -2
Explanation
The slope-intercept form of a linear function is y = mx + b, where m represents the slope and b represents the y-intercept. In the given function y = -5x - 2, the coefficient of x (-5) represents the slope and the constant term (-2) represents the y-intercept. Therefore, the correct answer is m = -5 and b = -2.
8.
If you double the slope of the function y=2x + 4, what effect will it have on the line?
Correct Answer
C. The line will become more steep.
Explanation
If you double the slope of the function y=2x + 4, it means that the coefficient of x, which represents the slope, will be multiplied by 2. This will result in a steeper line because the slope determines how steep or flat the line is. Doubling the slope will make the line increase more rapidly as x increases, causing it to become more steep.
9.
Which of the following functions is the steepest line?
y = 2x
y = 1/2x
y = 4x
y = 0.25x
Correct Answer
C. Y = 4x
Explanation
The function y = 4x is the steepest line because the coefficient of x is the largest among all the given functions. The greater the coefficient of x, the steeper the line.
10.
Changing the linear parent function y = x to y = x - 4 will shift the line down four units.
Correct Answer
A. True
Explanation
When a linear parent function y = x is changed to y = x - 4, it means that the y-coordinate of every point on the graph is reduced by 4 units. This results in shifting the entire line down by 4 units. Therefore, the statement "Changing the linear parent function y = x to y = x - 4 will shift the line down four units" is true.