Question

What is the equation of the line that passes through (3.-1) and is parallel to the line y = 3x + 2?​

Answer 1

`y=3x-10`

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 (the value of y when the line crosses the y-axis)
• Parallel lines always have the same slope and different y-intercepts

1) Determine the slope (m)

`y = 3x + 2`

From 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 slope, the line we're solving for will also have a slope of 3. Plug this into
`y=mx+b`:

`y=3x+b`

2) Determine the y-intercept (b)

`y=3x+b`

Plug in the given point (3,-1)

`-1=3(3)+b\\-1=9+b`

Subtract 9 from both sides

`-1-9=9+b-9\\-10=b`

Therefore, the y-intercept of the line is -10. Plug this back into
`y=3x+b`:

`y=3x-10`

I hope this helps!