Question

Given the following system of equations and their graph below, what can be determined about the slopes and y-intercepts of the system of equations? A line includes points 1 comma negative 3 and 3 comma negative 7. A line includes points 3 comma negative 7 and 6 comma negative 6. 4x + 2y = −2 x − 3y = 24 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.

Answer 1

The slopes are different, and the y-intercepts are different.

Explanation:

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Answer 2

The slopes are different, and the y-intercepts are different.

Explanation:

When we have an equation with the form: y=mx+b

m is the slope and b is the intercept.

So, for the first equation: 4x + 2y = -2, we can solve for y as:

`4x+2y=-2\\2y=-4x-2\\y=(-4x-2)/(2)\\ y=-2x-1`

Then, the slope of this equation is -2 and the intercept is -1

At the same way, for the second equation: x-3y=24, we can solve for y as:

`x-3y=24\\-3y=-x+24\\y=(-x+24)/(-3) \\y=(1)/(3)x-8`

Then the slope of this equation is
`(1)/(3)` and the intercept is -8

Finally, we can conclude that the slopes are different, and the y-intercepts are different.