Question

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

Answer 1

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

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

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

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)!