SOLUTION: 1. write an equation of the line that passes through (4,1) and has a slope of 2/3? 2.write an equation of the line that passes through (7,3) and (-2,9). 3. write an equation

Question 172154This question is from textbook
: 1. write an equation of the line that passes through (4,1) and has a slope of 2/3?
2.write an equation of the line that passes through (7,3) and (-2,9).
3. write an equation of the line that passes through (17,5) and intercepts the x axis at 7.
This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
where is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get

Add 1 to both sides to isolate y

Combine like terms and to get (note: if you need help with combining fractions, check out this solver)

------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of which goes through the point (,) is:

which is now in form where the slope is and the y-intercept is

Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver )

Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.

# 2

First let's find the slope of the line through the points

and

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 3 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

Simplify

So the equation that goes through the points

and

# 3

Note: the x intercept 7 is simply the point (7,0)

First let's find the slope of the line through the points

and

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 5 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

Simplify

So the equation that goes through the points

and

is

RELATED QUESTIONS
Write an equation of the line that passes through the point (2,-3) and has a slope of... (answered by ReadingBoosters)

Write an equation of the line that passes through the point (2,-3) and has a slope of... (answered by ReadingBoosters)

Write an equation in slope-intercept form of the line that passes through the point (-4,... (answered by solver91311)

write an equation of the line that has slope 2/3 and passes through point... (answered by College Student)

write an equation of the line that has slope 2/3 and passes through point (-6,4) (answered by Alan3354)

write an equation of the line that has slope 2/3 and passes through point... (answered by nerdybill)

Write an equation of the line that has slope 2/3 and passes through point... (answered by Fombitz)

Write an equation of the line that has slope 2/3 and passes through point... (answered by jim_thompson5910)

Write an equation of the line that has slope of 3 and passes through the point (4, -... (answered by ikleyn)