Question

Write an equation of the line that passes through the given point and is parallel to the given line.

Answer 1

Answer:

Part 40) $y=-2x+9$

Part 41) $y=5x+6$

Part 42) $y=\frac{2}{3}x+\frac{4}{3}$

Step-by-step explanation:

Remember that

If two lines are parallel, then their slopes are the same

Part 40) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (4,1)

Given line y=-2x+7

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

so

The slope of the given line is

$m=-2$

step 2

Find the y-intercept b

we have

$m=-2$

$(4,1)$

substitute in the linear equation

$1=(-2)4+b$

solve for b

$b=1+8$

$b=9$

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

$m=-2$

$b=9$

substitute

The equation of the line is

$y=-2x+9$

Part 41) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (0,6)

Given line y=5x-3

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

so

The slope of the given line is

$m=5$

step 2

Find the y-intercept b

$b=6$ ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

$m=5$

$b=6$

substitute in the linear equation

$y=5x+6$

Part 42) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (-5,-2)

Given line y=(2/3)x+1

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

so

The slope of the given line is

$m=\frac{2}{3}$

step 2

Find the y-intercept b

we have

$m=\frac{2}{3}$

$(-5,-2)$

substitute in the linear equation

$-2=(\frac{2}{3})(-5)+b$

solve for b

$-2=-\frac{10}{3}+b$

$b=-2+\frac{10}{3}$

$b=\frac{4}{3}$

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

$m=\frac{2}{3}$

$b=\frac{4}{3}$

substitute

The equation of the line is

$y=\frac{2}{3}x+\frac{4}{3}$