1.
Find the slope for 9x - 3y= 5
Correct Answer
slope is 3
3
m = 3
m=3
Explanation
The slope of a line can be found by rearranging the equation into slope-intercept form (y = mx + b), where m represents the slope. In the given equation, 9x - 3y = 5, we can rearrange it to -3y = -9x + 5 and then divide both sides by -3 to get y = 3x - 5/3. Comparing this with the slope-intercept form, we can see that the slope is 3. Therefore, the correct answer is "slope is 3, 3, m = 3, m = 3".
2.
Find the slope: 3x + 2y = 6
Correct Answer
-3/2
-1.5
m = -3/2
m = -1.5
m=-3/2
Explanation
The given equation is in the form of a linear equation, where the coefficients of x and y represent the slope of the line. In this case, the coefficient of x is 3 and the coefficient of y is 2. To find the slope, we can rearrange the equation to isolate y: 2y = -3x + 6. Dividing both sides by 2, we get y = (-3/2)x + 3. Therefore, the slope of the line is -3/2 or -1.5.
3.
Find the slope:x + 5y = 15
Correct Answer
-1/5
-.2
-.20
m = -1/5
m = -.2
m=-1/5
Explanation
The given equation is in the form of a linear equation, where the coefficient of x represents the slope of the line. In this case, the coefficient of x is 1, and the coefficient of y is 5. To find the slope, we need to isolate the coefficient of y. By rearranging the equation, we get 5y = -x + 15. Dividing both sides by 5, we get y = (-1/5)x + 3. Therefore, the slope of the line is -1/5. The answer choices -1/5, -.2, and -.20 all represent the same slope value, and the representations m = -1/5 and m = -.2 are also correct.
4.
Find the slope and x & y intercepts for 2x - y = 5
Correct Answer
E. M = 2 (0, -5) (5/2, 0)
Explanation
The given equation is in the form y = mx + b, where m represents the slope and (0, b) represents the y-intercept. In this case, the equation is 2x - y = 5, which can be rewritten as y = 2x - 5. Therefore, the slope is 2 and the y-intercept is (0, -5). Additionally, the x-intercept can be found by setting y = 0 and solving for x, which gives x = 5/2. So the x-intercept is (5/2, 0). Therefore, the correct answer is m = 2 (0, -5) (5/2, 0).
5.
Find the slope and x & y intercepts for 3x - 8y = -24
Correct Answer
D. M = 3/8 (0, 3) (-8, 0)
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 can determine the slope and the x and y intercepts. In this case, the equation is already in the desired form. The slope (m) is 3/8, which means that for every increase of 8 in the x-coordinate, the y-coordinate increases by 3. The y-intercept is 3, which means that the line intersects the y-axis at the point (0, 3). The x-intercept is -8, which means that the line intersects the x-axis at the point (-8, 0).
6.
Find the slope and x & y intercepts for -5x + 3y = 12
Correct Answer
D. M = 5/3 (0, 4) (-12/5, 0)
Explanation
The equation -5x + 3y = 12 can be rearranged to y = (5/3)x + 4. The slope of the line is 5/3, indicating that the line increases by 5 units vertically for every 3 units it moves horizontally. The y-intercept is (0, 4), which means that the line intersects the y-axis at the point (0, 4). The x-intercept is (-12/5, 0), indicating that the line intersects the x-axis at the point (-12/5, 0).
7.
Find the slope for 8x + 5y = 7
Correct Answer
-8/5
m = -8/5
m=-8/5
Explanation
The slope of a line can be found by rearranging the equation into slope-intercept form, y = mx + b, where m is the slope. In this case, we need to rearrange the equation 8x + 5y = 7. By isolating y, we get 5y = -8x + 7. Dividing both sides by 5, we have y = (-8/5)x + 7/5. Comparing this equation with y = mx + b, we can see that the slope, m, is -8/5. Therefore, the correct answer is -8/5.
8.
Find the slope for 6x - 3y = 5
Correct Answer
2
m = 2
m=2
Explanation
The slope of a linear equation can be found by rearranging the equation into slope-intercept form, y = mx + b, where m represents the slope. In the given equation, 6x - 3y = 5, we can rearrange it to -3y = -6x + 5 and then divide both sides by -3 to get y = 2x - 5/3. Comparing this equation to the slope-intercept form, we can see that the slope, m, is equal to 2. Therefore, the correct answer is m = 2.
9.
Find the x intercept for 8x + 9y = -16
Correct Answer
A. (-2, 0)
Explanation
The x-intercept of a linear equation is the point where the line intersects the x-axis. To find the x-intercept, we set y=0 and solve for x. Plugging in y=0 into the equation 8x + 9y = -16, we get 8x + 9(0) = -16. Simplifying this equation gives us 8x = -16, and dividing both sides by 8 gives x = -2. Therefore, the x-intercept is (-2, 0).
10.
Find the x intercept 9x - 7y = 27
Correct Answer
B. (3, 0)
Explanation
The x-intercept of a line is the point where the line crosses the x-axis, meaning the y-coordinate is 0. To find the x-intercept, we set y = 0 in the equation 9x - 7y = 27 and solve for x. When y = 0, the equation becomes 9x - 7(0) = 27, simplifying to 9x = 27. Dividing both sides by 9 gives x = 3. Therefore, the x-intercept is (3, 0).
11.
Find the y intercept 9x - 7y = 27
Correct Answer
C. (0, -27/7)
Explanation
The y-intercept of a linear equation is the point where the line intersects the y-axis. To find the y-intercept, we set x = 0 and solve for y. In this equation, when x = 0, we have 9(0) - 7y = 27, which simplifies to -7y = 27. Dividing both sides by -7, we get y = -27/7. Therefore, the y-intercept is (0, -27/7).
12.
Find the y intercept 5x + 10y = 35
Correct Answer
D. (0, 7/2)
Explanation
The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x=0 in the equation and solve for y. When we substitute x=0 into the equation 5x + 10y = 35, we get 10y = 35. Solving for y, we find y = 7/2. Therefore, the y-intercept is (0, 7/2).