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.

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mariacsinning mariacsinning · Answer 1 · 2020-05-10T05:53:44+02:00

Answer:

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

Step-by-step 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:

[tex]4x+2y=-2\\2y=-4x-2\\y=\frac{-4x-2}{2}\\ y=-2x-1[/tex]

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:

[tex]x-3y=24\\-3y=-x+24\\y=\frac{-x+24}{-3} \\y=\frac{1}{3}x-8[/tex]

Then the slope of this equation is [tex]\frac{1}{3}[/tex] and the intercept is -8

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

DragonWriter DragonWriter · Answer 2 · 2021-02-25T16:07:15+01:00

Answer:

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

Step-by-step explanation:

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