Question

What is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15?

Answer 1

Step 1: 3x + 4y = 15
Step 2: Get in Slope intercept form = y=mx+b
Step 3: Subtract 3x from both sides since your trying to get Y alone
Step 4: 4y = -3x + 15
Step 5: Divide 4 from both sides since 4 cannot go into -3 or 15 leave it as is
Step 6: Y =
`- \frac {3}{4}` +
`(15)/(4)`
Step 7: Point slope form= y-y=m(x-x)
Step 8: (8, -2) are your points 8x and -2y
Step 9: Substitute
Step 10: y - 2 =
`-(3)/(4)` (x - 8)
Step 11: Distribute
Step 12: y - 2 =
`-(3)/(4) x` + -6
Step 13: Add 2 to both sides
Answer : y =
`- (3)/(4) x` + 4

Answer 2

Answer:
`3x+4y=16`

Explanation:

Given equation of a line =
`3x + 4y = 15`

i.e.
`4y = 15-3x`

i.e.
`y=(15)/(4)-(3)/(4)x`

i.e.
`y=-(3)/(4)x+(15)/(4)` (1)

It is in intercept form
`y=mx+c` (2) , where m is slope.

By comparing (1) and (2) the slope of line :
`m=-(3)/(4)`

Also the parallel lines have same slope .

The equation of a line passing through a point (a,b) and having a slope of 'm' is given by :-

`(y-b)= m(x-a)`

Then the equation of the line that passes through (8,-2) and having slope of
`m=-(3)/(4)` is given by :-

`(y-(-2))=- (3)/(4)(x-8)`

`4(y+2)=-3(x-8)`

`4y+8=-3x+24`

`3x+4y=24-8`

`3x+4y=16`

Hence , the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is
`3x + 4y = 15` is
`3x+4y=16`

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