Question

Write the equation of the line that passes through the point (-3, 6) and is parallel to the line

Answer 1

Answer:

$y=\displaystyle\frac{1}{2}x+\displaystyle\frac{15}{2}$

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 of the line and b is the y-intercept (the value of y when the line crosses the x-axis).

• Parallel lines always have the same slope (m)

1) Determine the slope (m)

$y=\displaystyle\frac{1}{2} x+5$

From the given equation, we can tell that the slope is $\displaystyle\frac{1}{2}$. Because parallel lines always have the same slope, the slope of the line we're solving for is therefore $\displaystyle\frac{1}{2}$ as well. Plug this into $y=mx+b$:

$y=\displaystyle\frac{1}{2}x+b$

2) Determine the y-intercept (b)

$y=\displaystyle\frac{1}{2}x+b$

We're given that the line passes through the point (-3,6). Plug this into $y=\displaystyle\frac{1}{2}x+b$ and solve for b:

$6=\displaystyle\frac{1}{2}(-3)+b\\\\6=\displaystyle\frac{-3}{2}+b\\\\b=\frac{15}{2}$

Therefore, the y-intercept is $\displaystyle\frac{15}{2}$. Plug this back into $y=\displaystyle\frac{1}{2}x+b$:

$y=\displaystyle\frac{1}{2}x+\displaystyle\frac{15}{2}$

I hope this helps!

Answer 2

Answer:

$\because \:l_{1} \parallel \: l_{2} \\ \therefore m_{1} = m_{2} = \frac{1}{2} \\ \frac{y - 6}{x + 3} = \frac{1}{2} \\ y - 6 = \frac{1}{2}x + \frac{3}{2} \\ y = \frac{1}{2}x + \frac{3}{2} + 6\\ y = \frac{1}{2}x + \frac{15}{2}$