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3 years ago

What solution is y = 2x + 2 y = -2x + 4 ?

Mathematics

1 answer:

brilliants [131]3 years ago

6 0

Answer:

x = $\frac{1}{2}$ , y = 3

Step-by-step explanation:

y = 2x + 2 → (1)

y = - 2x + 4 → (2)

Substitute y = 2x + 2 into (2)

2x + 2 = - 2x + 4 ( add 2x to both sides )

4x + 2 = 4 ( subtract 2 from both sides )

4x = 2 ( divide both sides by 4 )

x = $\frac{2}{4}$ = $\frac{1}{2}$

Substitute this value into (1) for value of y

y = 2( $\frac{1}{2}$ ) + 2 = 1 + 2 = 3

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Hi, I'm happy to help!

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m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show rise, over the difference in the x points to show run.

Now, to find the slope we insert our values, starting with our second y point:

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m= $\frac{2-4 }{x_{2} -x_{1} }$

Now we insert our second x point:

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m= $\frac{-2 }{-6}$

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Now, we simplify our fraction by dividing the top and bottom by 2:

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So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y= $\frac{1}{3}$ x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Insert our values:

m= $\frac{4-1}{2-(-4)}$

Get rid of the double negative:

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Solve:

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Simplify:

m= $\frac{1}{2}$

Now that we know our slope, let's plug it in to our slope intercept form equation.

y= $\frac{1}{2}$ x+3

I hope this was helpful! Keep learning! :D

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