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ICE Princess25 [194]
3 years ago
5

Which is the equation of a line that is parallel to 2x + 5y = 4 and goes through the point (5, –4) ?

Mathematics
2 answers:
san4es73 [151]3 years ago
5 0

<em><u>Answer:</u></em>

y = \frac{-2}{5} x - 2

<em><u>Explanation:</u></em>

<u>The general formula of the linear equation is:</u>

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

<u>1- getting the slope of the given line:</u>

<u>The given line is:</u>

2x + 5y = 4

<u>Rearrange to be in the general formula:</u>

5y = -2x + 4 .............> y = \frac{-2}{5} x + 4

<u>slope of the given line is</u> : \frac{-2}{5}

<u>2- getting the slope of the required line:</u>

We are given that the two lines are parallel, this means that they have equal slopes.

<u>Therefore:</u>

<u>slope of the required line</u> = \frac{-2}{5}

<u>The equation of the required line now became</u> : y = \frac{-2}{5}x + c

<u>3- getting the value of c:</u>

We are given that the line passes through the point (5,-4). This means that this point satisfies the equation of the line.

<u>Therefore, we will substitute with the point in the equation and solve for c as follows:</u>

y = \frac{-2}{5}x + c

-4 = \frac{-2}{5} (5) + c

-4 = -2 + c

c = -4 + 2

c = -2

<u>Based on the above, the equation of the line is:</u>

y = \frac{-2}{5} x - 2

Hope this helps :)

barxatty [35]3 years ago
4 0

we know that

if two lines are parallel

then

their slopes are equal

Step 1

Find the slope of the line 2x + 5y = 4

2x + 5y = 4------> 5y=4-2x-----> y=(4/5)-(2/5)x------> slope m=(-2/5)

step 2

with m=-2/5 and the point (5, –4) find the equation of the line

y-y1=m*(x-x1)------> y+4=(-2/5)*(x-5)----> y=(-2/5)x+2-4

y=(-2/5)x-2

therefore

the answer is the option D

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