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

Answer: $3x+4y=16$

Step-by-step explanation:

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

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

i.e. $y=\dfrac{15}{4}-\dfrac{3}{4}x$

i.e. $y=-\dfrac{3}{4}x+\dfrac{15}{4}$  (1)

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

By comparing (1) and (2) the slope of line : $m=-\dfrac{3}{4}$

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 $m=-\dfrac{3}{4}$ is given by :-

$(y-(-2))=- \dfrac{3}{4}(x-8)$

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

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

$3x+4y=24-8$

$3x+4y=16$

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 $3x+4y=16$

.

Answer 2

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 = $- \frac {3}{4}$ + $\frac{15}{4}$
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 = $-\frac{3}{4}$ (x - 8)
Step 11: Distribute
Step 12: y - 2 =$-\frac{3}{4} x$ + -6
Step 13: Add 2 to both sides
Answer : y = $- \frac{3}{4} x$ + 4