Question

Which choice is the equation of a line that passes through (9, -3) and is parallel to the line represented by this equation?

Answer 1

A
Parallel lines have the same slope which is 5/3 so it can be a or b

A (9,-3) put 9 in X and -3 on y
Y= 5/3x-18
-3= 5/3(9)-18
-3= 15-18
-3= -3

Answer 2

Answer:

A. $y=\frac{5}{3}x-18$

Step-by-step explanation:

We know that,

The general form of a linear equation is given by

$y=mx+b$, where m= slope and b = y-intercept.

Since, the given equation of a line is $y=\frac{5}{3}x-4$

So, the slope of the given line is $m=\frac{5}{3}$

Further, we know that,

The slopes of two parallel lines are equal.

Thus, the slope of the line parallel to the given line is $\frac{5}{3}$

That is, the equation of the new line is $y=\frac{5}{3}x+b$

Since, this line passes through the point (9,-3).

So, we have,

$-3=\dfrac{5}{3}\times 9+b\\\\-3=15+b\\\\b=-3-15\\\\b=-18$

Hence, the required equation of the line is $y=\frac{5}{3}x-18$.

So, option A is correct.