Question

What is the equation of the line that is parallel to the line y = - 1/3x + 4 and passes through the point (6, 5)?

Answer 1

Answer:

$y=-\frac{1}{3}x+7$

Step-by-step explanation:

we know that

If two lines are parallel then their slopes are equal

The equation of the given line is

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

the slope is $m=-\frac{1}{3}$

so

the slope of the parallel line to the given line is also $m=-\frac{1}{3}$

Find the equation of the line that is parallel to the given line and passes through the point (6, 5)

we have

$m=-\frac{1}{3}$

$point\ (6,5)$

The equation of the line in point slope form is

$y-y1=m(x-x1)$

substitute

$y-5=-\frac{1}{3}(x-6)$

Convert to slope intercept form

$y=mx+b$

isolate the variable y

$y-5=-\frac{1}{3}x+2$

$y=-\frac{1}{3}x+2+5$

$y=-\frac{1}{3}x+7$