Algebra 1 Common Core Student Edition, Grade 8-9

Pr o b l em 4 Writing an Equation From Two Points

Think
Can you use eith er
point to find the
y-intercept?
Yes. You can substitute
the slope and the
coordinates o f any point
on the line into the form
y = mx + b and solve
for fa.

What information can

you use?

The slope tells you the

ratio o f vertical change

to horizontal change. Plot

the y-intercept. Then use

the slope to plot another

point on the line.

What equation in slope-intercept form represents the line that passes through the

points (2,1) and (5, - 8 )?

Know Need

The line passes through An equation o f the

(2 ,1 ) and ( 5 , - 8 ). line

Step 1 Use th e two points to find the slope.

slope = 5 _ -8-1 2 ~ = - g - = —3 -9

Step 2 Use th e slope an d th e coordinates of one of th e points to find b.

y = mx + b Use s lo p e -in te rc e p t fo rm.

1 = - 3 ( 2 ) + b Substitute -3 for m, 2 for x, and 1 for y.

7 = b Solve for b.

Step 3 S ubstitute th e slope an d y-intercept into th e slope-intercept form,

y = mx + b Use s lo p e -in te rc e p t fo rm ,

y = -3jc + 7 Substitute -3 for m and 7 for b.

An e q u a tio n of th e line is y = - 3 x + 7.

v G o t It? 4. W hat eq u a tio n in slope-intercept form represents th e line th a t passes

through th e points (3, - 2 ) an d (1, - 3 )?

Mm

Use the tw o points to find the slope.

Then use the slope and one p oin t to

solve fo r the y-intercept.

You can use th e slope an d y -in terc ep t from a n equ atio n to graph a line.

Graphing a Linear Equation

What is the graph of y = 2x — 1?

Step 1 The y - in te rc e p t is

• 
  
  
  
  1. So p lo t a p o in t
     at (0, -1 ).
  
  
  
  

Step 2 The slo p e is 2, o r y.

M o v e up 2 u n its a nd

right 1 unit. Plot

another point.

Step 3 D ra w a lin e th r o u g h

the tw o points.

& G o t It? 5. W hat is the graph of each linear equation?

a. y = — 3jc + 4 b. y = 4x — 8

3 1 0 Ch ap t er s Linear Funct ions