Question

Write the equation of the line parallel to 3x-y=7 that passes through point(-5,-3)

Answer 1

Answer:

y - 3x = 12 is  the equation of the line parallel to 3x-y=7 that passes through point(-5,-3).

Step-by-step explanation:

we have given the equation of line

3x - y = 7  

equation in standard form:

y = 3x - 7

The slope of this equation is m = 3, this is also the slope of the parallel line since parallel lines have equal slopes. we also have a point ( -5 , -3 ).

therefore we write this equation as follow:

y - y₀ = m ( x - x₀)

y - (- 3 ) = 3 (x - ( -5 ) )

y + 3 = 3 ( x + 5)

y + 3 = 3x + 15

y - 3x = 15 -3

y - 3x = 12 is the required result.

Answer 2

Answer:

$\boxed{y-3x=12}$

Step-by-step explanation:

In this problem we know the equation of a line, which is:

$3x-y=7$

We also can write this equation as:

$y=3x-7$

The slope of this line is $m=3$ which is the slope of the line we are looking for because they're parallel. We also have a point $(-5,-3)$. Therefore, we can write this equation as follows:

$y-y_{0}=m(x-x_{0}) \\ \\ y-(-3)=3(x-(-5)) \\ \\ y+3=3(x+5) \\ \\ y+3=3x+15 \\ \\ \boxed{y-3x=12}$

From the figures below, the line in red is $3x-y=7$ while the line in blue is $y-3x=12$ and this line passes through the point (-5, -3)!