Which equation has the same slope as
y=4x-5
A.4x-2y=0
B.3y-12x=21
C.y=5x+7
D.5y=4x-6
To determine which equation has the same slope as y = 4x - 5, we need to rewrite all the given equations in slope-intercept form, which is y = mx + b, where m represents the slope.
A. 4x - 2y = 0
To rewrite this equation in slope-intercept form, we need to isolate y:
4x - 2y = 0
-2y = -4x
y = 2x
The slope of this equation is 2, so it does not have the same slope as y = 4x - 5.
B. 3y - 12x = 21
To rewrite this equation in slope-intercept form, we need to isolate y:
3y - 12x = 21
3y = 12x + 21
y = 4x + 7
The slope of this equation is 4, so it does not have the same slope as y = 4x - 5.
C. y = 5x + 7
The slope of this equation is 5, which is the same slope as y = 4x - 5.
Therefore, the equation y = 5x + 7 has the same slope as y = 4x - 5.
D. 5y = 4x - 6
To rewrite this equation in slope-intercept form, we need to isolate y:
5y = 4x - 6
y = (4/5)x - 6/5
The slope of this equation is 4/5, which is not the same as the slope of y = 4x - 5.
In conclusion, the equation that has the same slope as y = 4x - 5 is C. y = 5x + 7.
To determine which equation has the same slope as y = 4x - 5, we need to compare the given options with the slope-intercept form: y = mx + b, where m represents the slope.
In the equation y = 4x - 5, we can see that the slope is 4. Therefore, we need to find an equation with the same slope (4). Let's go through each option:
A. 4x - 2y = 0:
To convert this equation into slope-intercept form, we need to solve for y. Rearranging the equation, we get: 2y = 4x - 0, or y = 2x + 0. We see that the slope (2) is not the same as the original equation, so this option is not the correct answer.
B. 3y - 12x = 21:
Again, solving for y by rearranging the equation, we get: 3y = 12x + 21, or y = 4x + 7. As we compare the slope (4) with the original equation, we can see that this option has the same slope, so it is a potential answer.
C. y = 5x + 7:
This equation already has the slope-intercept form, y = mx + b. Comparing the slope of this equation (5) with the original equation, we see that it does not match, so this option is not the correct answer.
D. 5y = 4x - 6:
Now, let's rearrange this equation to get it in slope-intercept form. Dividing each term by 5, we have: y = (4/5)x - 6/5. In this equation, the slope is 4/5. Therefore, it does not match the slope of the original equation, so it is not the correct answer.
In conclusion, the equation that has the same slope as y = 4x - 5 is option B: 3y - 12x = 21.