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4 years ago

What is the equation of the line that is parallel to 8x-5y=2 and goes through the point (-5,-2)

Mathematics

1 answer:

Stella [2.4K]4 years ago

3 0

Answer:

8x - 5y = - 30

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 8x - 5y = 2 into this form

Subtract 8x from both sides

- 5y = - 8x + 2 ( divide all terms by - 5 )

y = $\frac{8}{5}$ x - $\frac{2}{5}$ ← in slope- intercept form

with slope m = $\frac{8}{5}$

• Parallel lines have equal slopes, hence

y = $\frac{8}{5}$ x + c ← is the partial equation of the parallel line

To find c substitute (- 5, - 2) into the partial equation

- 2 = - 8 + c ⇒ c = - 2 + 8 = 6

y = $\frac{8}{5}$ x + 6 ← in slope- intercept form

Multiply through by 5

5y = 8x + 30 ( subtract 5y from both sides )

0 = 8x - 5y + 30 ( subtract 30 from both sides )

8x - 5y = - 30 ← in standard form

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Compare and Contrast Graph y = 2x + 5 and y=-13x+5. Describe how these lines are alike and how they are different. *

krek1111 [17]

Here are a couple I found:

Similarities:

They have the same y-intercept of (0,5).
They are both in slope-intercept form.

Differences:

The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right.
They have different x-intercepts. (y = 2x + 5 intersects (- $\frac{5}{2}$ , 0) while y = -13x + 5 intersects at ( $\frac{5}{13}$ , 0)

Explanation:

Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).

As for differences, we can see that the coefficient in place of that "m" is positive in y = 2x + 5 and negative in y = -13x + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.

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NNADVOKAT [17]

You need to implement the process of "flip-flop" and multiply which is where you flip the second fraction and multiply.

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Now you multiply across. 2×15=30 and 3×11=33

So now it is $\frac{30}{33}$

-----------------------------------------------------------
To reduce to the lowest terms, find the GCF common factor

The GCF is 3

Divide both the numerator and denominator by 3

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Answer:

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Step-by-step explanation:

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