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?

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

JeanaShupp JeanaShupp · Answer 2 · 2020-01-05T08:20:14+01:00

Answer: [tex]3x+4y=16[/tex]

Step-by-step explanation:

Given equation of a line = [tex]3x + 4y = 15[/tex]

i.e. [tex]4y = 15-3x[/tex]

i.e. [tex]y=\dfrac{15}{4}-\dfrac{3}{4}x[/tex]

i.e. [tex]y=-\dfrac{3}{4}x+\dfrac{15}{4}[/tex] (1)

It is in intercept form [tex]y=mx+c[/tex] (2) , where m is slope.

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

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 :-

[tex](y-b)= m(x-a)[/tex]

Then the equation of the line that passes through (8,-2) and having slope of [tex]m=-\dfrac{3}{4}[/tex] is given by :-

[tex](y-(-2))=- \dfrac{3}{4}(x-8)[/tex]

[tex]4(y+2)=-3(x-8)[/tex]

[tex]4y+8=-3x+24[/tex]

[tex]3x+4y=24-8[/tex]

[tex]3x+4y=16[/tex]

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

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