Question

Consider the point (−8,3) and the line
2x + 3y = 5.
Find the equation of the line through the
point and parallel to the given line. The options are
A. None of these
B. 2x − 3y = −7
C. 2y − 3x = −7
D. 2x + 3y = −7
E. 2x − 3y = 7
F. 2y + 3x = 7

Answer 1

2x+3y=-7

Answer 2

Because 2x+3y=5 is the same as \[y=\frac{ -2x }{ 3 }+\frac{ 5 }{ 3 }\]

Answer 3

We want a line that's parallel to the first line so the slope has to be the same. So the only thing we can change of the second line is the y intercept.

Answer 4

For the second line at the value x=-8 the y has to be 3

So if we plug in -8 into \[y=\frac{ -2x }{ 3 }+\frac{ 5 }{ 3 }\]
we get 7. So For the first line at the value of x=-8 the y is 7. That's 4 y units too high, so let's take four from the y intercept \[y=\frac{ -2x }{ 3 }+(\frac{ 5 }{ 3 }-4)\]

that equals \[y=\frac{ -2x }{ 3}-\frac{ 7 }{ 3 }\]

Which is the same as answer D.

Answer 5

put it in y = mx + b where m is the slope
2x + 3y = 5
3y = -2x + 5
y = -2/3x + 5/3
The slope -2/3 will be the same because the line is parallel.

now put it in this form : y - y1 = m(x - x1)
using slope -2/3 and points (-8,3)
y - 3 = -2/3(x - (-8)
y - 3 = -2/3(x + 8)
y - 3 = -2/3x - 16/3
2/3x + y = 3 - 16/3
2/3x + y = 9/3 - 16/3
2/3x + y = - 7/3 (multiply by 3 to get rid of the fractions)
2x + 3y = - 7
ANSWER : D

Answer 6

d