SOLUTION: Write an equation for the line that passes through (2,1) and (3,5)

Question 544699: Write an equation for the line that passes through (2,1) and (3,5)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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

and

Note:

is the first point

. So this means that and .
Also,

is the second point

. So this means that 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 1 to both sides.

Combine like terms.

So the equation that goes through the points

and

is

Notice how the graph of goes through the points

and

. So this visually verifies our answer.
Graph of through the points

and

RELATED QUESTIONS
Write an equation in slope-intercept form for the line that passes through (-1, -2) and... (answered by josgarithmetic,ikleyn,MathTherapy)

Find an equation for the line that passes through the points (5, -4) and (1,... (answered by jim_thompson5910)

Write an equation for the line that passes through (3, 14) and is parallel to the line... (answered by MathLover1)

[ write an equation for the line that is parallel to the given line and that passes... (answered by TimothyLamb)

Write an equation for the line that passes through the points (12, 3) and (�3,... (answered by ewatrrr)

write the equation of the line that passes through (0, 5(1/2)) and (-3(1/2),... (answered by stanbon,mananth)

Write an equation of the line that passes through the points (-5,3) and... (answered by jim_thompson5910,checkley77)

write an equation in slope-intercept form for the line that satisfies each set of... (answered by funmath)

Write the slope-intercept equation for the line that passes through (1, -9) and (3, -1). (answered by ewatrrr)