Write an equation for the line parallel to the line – 8x + 4y = 4 through the point (-6,3). Please enter your answer in slope intercept form

Question

Write an equation for the line parallel to the line – 8x + 4y = 4 through the point (-6,3). Please enter your answer in slope intercept form or standard form.

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Bella 1 week 2021-10-06T10:10:52+00:00 1 Answer 0

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    2021-10-06T10:12:03+00:00

    Answer:

    y = 2x + 15     OR    2x- y +15 =0

    Step-by-step explanation:

    To find the equation for the line parallel to the line -8x + 4y = 4, passing through the point (-6,3), we will first make the equation given to be in slope-intercept form, so that we can find the slope of this line

    -8x + 4y = 4 we have to change it to the form y=mx + c

    To do that, lets add 8x to both-side of the equation

    8x -8x +4y=8x+4

    4y=8x+4

    divide both-side of the equation by 4

    4y/4  = 8x/4  +4/4

    y=2x + 1

    comparing the above equation with y=mx + c

    our slope(m) = 2

    Any equation parallel to this line will have the same slope, so the slope(m) of our new equation will also be 2

    Now we need to find the intercept of our new equation, to do that we will plug in the points given and our new slope into y=mx + c and find the value of our intercept(c)

    The points given are x=-6 and y=3 and our new slope is m=2

    plugging in our variables, thus;

    y =mx + c

    3 = 2(-6) + c

    3 = -12 + c

    add 12 to both-side of the equation

    3+12 = -12+12+c

    15=c

    c=15

    Therefore our intercept for the new equation is 15

    To form our new equation, we will just plug in our new slope and intercept into y=mx + c

    y = 2x + 15    (this is in slope intercept form)

    we can rearrange it to be in standard form;

    2x- y-15=0

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