Question

Which of the following has the same slope as the equation Y=1/2x-10?

a
1/2x - y = 10
b
-x + 3y = 12
c
-1/2x + y = -10
d
-2x + y = -6

Answer 1

After converting each given equation to the slope-intercept form, it is clear that both the original equation Y=1/2x-10 and the option c, -1/2x + y = -10, have the same slope of 1/2.

Step-by-step explanation:

To determine which equation has the same slope as Y=1/2x-10, we rewrite each given equation in slope-intercept form (y = mx + b), where m represents the slope.

1. 1/2x - y = 10 can be rewritten as y = 1/2x - 10, which has a slope of 1/2.
2. -x + 3y = 12 can be rewritten as y = 1/3x + 4, so the slope is 1/3.
3. -1/2x + y = -10 can be rewritten as y = 1/2x - 10, which has a slope of 1/2.
4. -2x + y = -6 can be rewritten as y = 2x - 6, indicating a slope of 2.

Based on this analysis, the equations y = 1/2x - 10 and -1/2x + y = -10 both have the same slope of 1/2. Therefore, the correct answer is option c.

Answer 2

c. -1/2x + y = -10

Step-by-step explanation:

`- (1)/(2) x + y = - 10 \\ y = (1)/(2) x - 10`

Changing the order of the equation, you can verify the coefficient of x is the same when y is isolated.

In slope-intercept form, the coefficient of x, or the m in y=mx+b, is the slope or gradient.