Question

Select the equation of the line parallel to y= -3x -5 the equation and that passes through the point (1,2)

Answer 1

`y=-3x+5`

Explanation:

Hi there!

What we need to know:

• Linear equations are typically organized in slope-intercept form:
  `y=mx+b` where m is the slope and b is the y-intercept (b)
• Parallel lines always have the slope slopes and different y-intercepts

1) Determine the slope (m)

`y= -3x -5`

With the given line, we can identify clearly that -3 is in the place of m, making it the slope. Because parallel lines have the same slopes, the slope of the line we're currently solving for would also be -3. Plug this into
`y=mx+b`:

`y=-3x+b`

2) Determine the y-intercept (b)

`y=-3x+b`

Plug in the given point (1,2) and isolate b

`2=-3(1)+b\\2=-3+b`

Add 3 to both sides

`2+3=-3+b+3\\5=b`

Therefore, the y-intercept of the line is 5. Plug this back into
`y=-3x+b`:

`y=-3x+5`

I hope this helps!