Question

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

Answer 1

Answer:

$y=3x-10$

Step-by-step 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!

Answer 2

Answer:

y=3x-10

Step-by-step explanation: