1.
A line has an x-intercept of 4 and y-intercept of 7.- Write an equation in slope intercept form for the line
- Write an equation that is parallel to this line,
- Write an equation that is perpendicular to the line from part a.
2.
What is the y intercept of the line?
Correct Answer
B. 1
Explanation
The y-intercept of a line is the point where the line crosses the y-axis. In this case, the y-intercept is 1. This means that when x is equal to 0, the corresponding y value is 1.
3.
What is the slope of the line?
Correct Answer
A. Positive
Explanation
The slope of a line is a measure of how steep the line is. A positive slope means that the line is increasing as it moves from left to right. In other words, as the x-values increase, the y-values also increase. This can be visualized as a line that is slanting upwards from left to right on a graph.
4.
What is the slope of the line that passes through the points (-3,7) and (-9,4)?
Correct Answer
A. 1/2
Explanation
The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (-3,7) and (-9,4). Plugging these values into the formula, we get (4 - 7) / (-9 - (-3)) = -3 / -6 = 1/2. Therefore, the slope of the line is 1/2.
5.
Which line has a slope of 0?
Correct Answer
B. Line B
Explanation
Line B has a slope of 0 because a line with a slope of 0 is a horizontal line. In other words, the line does not rise or fall as it extends horizontally. The slope of a line is determined by the change in the y-coordinates divided by the change in the x-coordinates between any two points on the line. Since a horizontal line has the same y-coordinate for all points, the change in y is always 0, resulting in a slope of 0.
6.
Which line has an undefined slope?
Correct Answer
D. Line D
Explanation
Line D has an undefined slope because it is a vertical line. A vertical line has no change in the x-coordinate, resulting in a denominator of zero when calculating the slope using the formula (change in y / change in x). Since division by zero is undefined, the slope of a vertical line is undefined.
7.
The line y = -7 is:
Correct Answer
A. Horizontal
Explanation
The line y = -7 is horizontal because it has a fixed y-coordinate of -7, regardless of the value of x. In other words, all the points on this line have the same y-coordinate, while their x-coordinates can vary. This indicates that the line is parallel to the x-axis and does not have any vertical movement. Therefore, it can be concluded that the line y = -7 is horizontal.
8.
The line x = 5 is:
Correct Answer
B. Vertical
Explanation
The line x = 5 is vertical because it is a vertical line passing through the x-coordinate 5. Vertical lines have a constant x-coordinate and can intersect any y-coordinate, but they do not have a slope. In this case, the line x = 5 is a vertical line that intersects the y-axis at multiple points, making it a vertical line.
9.
Which graph shows the equation y = x + 4A.B.C.D.
Correct Answer
B. B
10.
Which of the following lines is not perpendicular to
Correct Answer
D. 2y = 5x + 1.5
Explanation
The equation 2y = 5x + 1.5 is not perpendicular to y = 0.4x - 7 because the slopes of the two lines are not negative reciprocals of each other. The given equation has a slope of 5/2, while the equation y = 0.4x - 7 has a slope of 0.4. For two lines to be perpendicular, their slopes must be negative reciprocals of each other, meaning that when multiplied together, they equal -1. Since 0.4 * (5/2) does not equal -1, the line 2y = 5x + 1.5 is not perpendicular to y = 0.4x - 7.
11.
Which equation represents a line that intersects at exactly one point?
Correct Answer
D. Y = (1/3)x - 3
Explanation
The equation y = (1/3)x - 3 represents a line that intersects the y-axis at -3 and has a slope of 1/3. Since the slope is not zero or undefined, the line will intersect the x-axis at exactly one point. Therefore, this equation represents a line that intersects at exactly one point.
12.
Which description best compares the graphs given by the equations 3x – y = 5 and 2x + 6y = 24?
Correct Answer
C. Perpendicular
Explanation
The given equations are 3x - y = 5 and 2x + 6y = 24. To determine the relationship between their graphs, we can rearrange both equations to slope-intercept form (y = mx + b). The first equation becomes y = 3x - 5, and the second equation becomes y = -1/3x + 4. The slopes of the two lines are 3 and -1/3, which are negative reciprocals of each other. When two lines have slopes that are negative reciprocals, they are perpendicular to each other. Therefore, the graphs of these equations are perpendicular.
13.
Which description best compares the graphs given by the equations x – 5y = -5 and 5x – 25y = 75?
Correct Answer
A. Parallel
Explanation
The given equations are in the form of linear equations. The equation x - 5y = -5 can be rewritten as y = (1/5)x + 1, while the equation 5x - 25y = 75 can be rewritten as y = (1/5)x - 3. Both equations have the same slope of 1/5, indicating that the graphs of the equations are parallel.
14.
Which equation represents a line parallel to the x-axis?
Correct Answer
A. Y = -5
Explanation
The equation y = -5 represents a line parallel to the x-axis because the y-coordinate remains constant (-5) for all values of x. In other words, no matter what the value of x is, the y-coordinate will always be -5. This indicates that the line is horizontal and does not have any vertical change. Thus, it is parallel to the x-axis.
15.
What is an equation of the line that passes through the point (3,−1) and has a slope of 2?
Correct Answer
A. Y = 2x + 5
Explanation
The equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is given as 2. The point (3, -1) lies on the line, so we can substitute these values into the equation. Plugging in x = 3 and y = -1, we get -1 = 2(3) + b. Solving for b, we find b = -7. Therefore, the equation of the line that passes through the point (3, -1) and has a slope of 2 is y = 2x + 5.
16.
Create a table of values for the equation , plot the points and graph the equationUse GeoGebra and share
Correct Answer
N/A
17.
Write the equation of the line that is parallel to y = -x + 4 and goes through the point (6,-3).
Correct Answer
N/A
Explanation
The equation of a line that is parallel to y = -x + 4 will have the same slope, which is -1. Using the point-slope form of a linear equation, we can plug in the coordinates of the given point (6,-3) and the slope (-1) to find the equation of the line. The equation will be y - (-3) = -1(x - 6), which simplifies to y + 3 = -x + 6.
18.
You start a lawn mowing service. You pay $75 for the lawn mower and plan on charging $25 per lawn. Write an equation to relate your income y to the number of lawns you mow x.
Correct Answer
N/A
Explanation
The equation to relate your income y to the number of lawns you mow x is y = 25x - 75. This equation represents the total income (y) you earn by mowing x number of lawns. The $75 is subtracted from the total income as it represents the initial cost of the lawn mower. The $25 per lawn is then multiplied by the number of lawns mowed to calculate the income from mowing lawns.