Question

What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y=-4/3x -1

Answer 1

Answer:

$y=\displaystyle-\frac{4}{3}x+22$

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
• Parallel lines always have the same slope (m)

Determine the slope (m):

$y=\displaystyle-\frac{4}{3}x -1$

The slope of the given line is $\displaystyle-\frac{4}{3}$, since it is in the place of m in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be $\displaystyle-\frac{4}{3}$. Plug this into y=mx+b:

$y=\displaystyle-\frac{4}{3}x+b$

Determine the y-intercept (b):

$y=\displaystyle-\frac{4}{3}x+b$

To find the y-intercept, plug in the given point (6,14) and solve for b:

$14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22$

Therefore, the y-intercept of the line is 22. Plug this back into $y=\displaystyle-\frac{4}{3}x+b$:

$y=\displaystyle-\frac{4}{3}x+22$

I hope this helps!