1.
Express the equation 3x - 2y = 12 in the form y = mx + b
Correct Answer
C. Y = 3/2x - 6
Explanation
The given equation 3x - 2y = 12 can be rearranged to solve for y. By subtracting 3x from both sides of the equation and then dividing by -2, we get -2y = -3x + 12. Dividing both sides by -2, we find that y = 3/2x - 6.
2.
Express the equation 5.4x - 1.80y + 3.6 = 0 in the form y = mx + b
Correct Answer
D. Y = 3x + 2
Explanation
The equation 5.4x - 1.80y + 3.6 = 0 can be rearranged to isolate the variable y. By moving the terms around, we get -1.80y = -5.4x - 3.6. Dividing both sides of the equation by -1.80, we find that y = 3x + 2. Therefore, the correct answer is y = 3x + 2.
3.
Which graph is the graph of the linear relation -4x + 6y = -12?
Correct Answer
B. Graph b
Explanation
The graph of the linear relation -4x + 6y = -12 can be determined by rearranging the equation to solve for y. By isolating y, we get y = (2/3)x - 2. This equation is in the form y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation with the equation of a straight line, we can see that the slope is 2/3 and the y-intercept is -2. Therefore, the correct graph would be the one that has a slope of 2/3 and a y-intercept of -2, which is Graph b.
4.
Which graph is the graph of the linear relation 1/3x - 3y + 1/6 = 0
Correct Answer
C. Graph c
Explanation
The given linear relation can be rearranged to the standard form of a linear equation, which is y = mx + b. In this case, the equation becomes y = (1/6)x - 1/18. By comparing the equation with the slope-intercept form, we can determine that the slope of the line is 1/6 and the y-intercept is -1/18. Looking at the graphs, Graph c is the only one that has a slope of 1/6 and intersects the y-axis at -1/18. Therefore, Graph c is the correct graph for the given linear relation.
5.
Use the graph to determine the slope and y-intercept of the line
Correct Answer
A. M = 5/2, b = -4
Explanation
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, the given equation is y = (5/2)x - 4. Therefore, the slope is 5/2 and the y-intercept is -4.
6.
Use the graph to determine the slope and y-intercept of the line
Correct Answer
D. M = -1/4, b = 2
Explanation
The slope of a line represents the rate of change of the line, or how steep it is. In this case, the slope is -1/4, which means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 1/4. The y-intercept, represented by the value of b, is the point where the line intersects the y-axis. In this case, the y-intercept is 2, which means that the line crosses the y-axis at the point (0, 2). Therefore, the correct answer is m = -1/4, b = 2.
7.
Describe the line whose equation is -2/3x - y = - 9
Correct Answer
C. The y-intercept of the line is 9. The slope of the line is negative and it falls 2 units for every 3 units it runs
Explanation
The given equation represents a line with a y-intercept of 9 and a slope of -2/3. This means that the line intersects the y-axis at the point (0, 9) and for every 3 units it runs horizontally (in the x-direction), it falls 2 units vertically (in the y-direction). Therefore, the correct answer is "The y-intercept of the line is 9. The slope of the line is negative and it falls 2 units for every 3 units it runs."
8.
Determine the slope and y-intercept of the line 6x - 2y + 10 = 0
Correct Answer
B. M = 3, b = 5
Explanation
The given equation is in the form y = mx + b, where m is the slope and b is the y-intercept. By rearranging the equation, we get -2y = -6x - 10, which simplifies to y = 3x + 5. Therefore, the slope (m) is 3 and the y-intercept (b) is 5.
9.
Determine the slope and y-intercept of the line 2.6x + 4.4y - 12.8 = 0
Correct Answer
C. M = -13/22, b = 32/11
Explanation
The given equation is in the form of Ax + By + C = 0, where A = 2.6, B = 4.4, and C = -12.8. To determine the slope and y-intercept, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
First, isolate the y term by subtracting 2.6x from both sides of the equation:
4.4y = -2.6x + 12.8
Next, divide both sides of the equation by 4.4 to solve for y:
y = (-2.6/4.4)x + (12.8/4.4)
Simplifying the equation gives us:
y = (-13/22)x + (32/11)
Comparing this equation to y = mx + b, we can see that the slope (m) is -13/22 and the y-intercept (b) is 32/11. Therefore, the correct answer is m = -13/22, b = 32/11.
10.
Dylan gets paid a flat rate of $10 per fare plus $0.25 for each km he drives his taxi. Which equation best represents this linear relation?
Correct Answer
D. Y = 0.25x + 10
Explanation
The equation y = 0.25x + 10 represents the linear relation between the amount Dylan gets paid (y) and the distance he drives his taxi (x). The flat rate of $10 per fare is represented by the constant term 10 in the equation. The additional $0.25 for each km is represented by the coefficient 0.25 of the x term in the equation. Therefore, this equation best represents the given situation.