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3 years ago

The equation of line q is 5y - 4x = 10. Write the standard fom of the equation of the line that fits the following description:

Mathematics

1 answer:

kumpel [21]3 years ago

7 0

<h3>Answer: -4x+5y = 100</h3>

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Explanation:

The given equation is the same as -4x+5y = 10

It is of the form Ax+By = C, where A = -4, B = 5, C = 10

Anything parallel to Ax+By = C is of the form Ax+By = D. The only difference is the C has changed to a D.

This means anything parallel to -4x+5y = 10 is -4x+5y = D, where D is not equal to 10, but it could be any other number.

Plug in the coordinates of (-15,8) to find the value of D

-4x+5y = D

-4(-15)+5(8) = D

60+40 = D

100 = D

D = 100

We have -4x+5y = D update to -4x+5y = 100

The equation -4x+5y = 100 is parallel to -4x+5y = 10, and it goes through (-15,8)

Parallel lines have the same slope, but different y intercepts.

Note how Ax+By = C has a slope of m = -B/A. This means A cannot be zero.

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krok68 [10]

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3 years ago

How do i find the slope

Elodia [21]

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

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:

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

Now insert our first y point:

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

Now we insert our second x point:

m= $\frac{2-4 }{-3 -x_{1} }$

And finally our first x point:

m= $\frac{2-4 }{-3 -3 }$

Now, we solve:

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

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

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

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

m= $\frac{1}{3}$

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