Math 8H
Standard Form
And
Word Problems
Heath text, section 5.5
Algebra 1
Glencoe McGraw-Hill
JoAnn Evans
Slope-Intercept Form of a Linear Equation:
y = mx + b
Point-Slope Form of a Linear Equation:
y – y1 = m(x – x1)
Standard Form of a Linear Equation
Ax + By = C
Remember that in Standard Form, both variable terms are on the
left side of the equal sign and the constant term is on the right
side. Another feature of the Standard Form is that all
coefficients are integers.
Write an equation in standard form of the line that
passes through the point and has the given slope.
Using y = mx + b
(  2, 4 ),
m  6
U sing y  y1  m(x  x1 )
(  2, 4 ),
m  6
y  mx  b
y  y1  m ( x  x1 )
4   6(  2 )  b
y  4   6  x  (  2) 
4  12  b
y  4   6( x  2)
8  b
y   6x  8
6x  y   8
y  4   6x  12
y   6x  8
6x  y   8
Candy corn costs $2 per pound at the candy store and
M&Ms cost $3 per pound. With $30 to spend, what are the
different amounts of the two candies that you can buy?
Let x = # pounds of M & Ms
Let y = # pounds of candy corn
Let 3x = VALUE of the M & Ms
Let 2y = VALUE of the candy corn
Value of the M
3x
&
Ms
+ Value of the candy corn = Total Cost
+
2y
= 30
3(0) + 2y = 30
y = 15
(all candy corn,
no M & M’s)
3x + 2(0) = 30
x = 10
(all M&Ms,
no
candy corn)
Candy Corn (in pounds)
Find the
x- and yintercepts.
16
14
12
10
8
6
4
2
0
2
4
6
8
10
12
14
16
M & M’s (in pounds)
Each point on the line represents a
combination of the 2 candies that would
have a total cost of $30.
Name some of the combinations.
Suppose you had $6.00 to buy bananas and apples.
Bananas cost $0.49 per pound and apples cost $0.34 per
pound. Write a linear equation that represents the
different amounts of fruit you could buy.
Let x = weight of bananas
Let 49x = VALUE of bananas
Let y = weight of apples
Let 34y = VALUE of apples
Value of
bananas
49x
+
Value of
apples
+
34y
= Total price
=
600
One possibility is that you could buy 10 pounds of
bananas. How many pounds of apples would then be
possible to buy?
49x + 34y = 600
49(10) + 34y = 600
490 + 34y = 600
-490
-490
34y = 110
y  3.2 lb
of apples
You are running for class president and have $48 to spend
on publicity for your campaign. It costs $2 to make a
campaign button and $1.20 to make a poster. Write an
equation that represents the different numbers of
buttons, x, and posters, y, that you could make.
Let x = # of buttons
Let 2x = VALUE of the buttons
Let y = # posters
Let 1.2y = VALUE of the posters
Value of buttons
2x
20x
5x
+
Value of posters
=
Total Cost
+
+
1.2y
12y
= 48
= 480
+
3y
= 120
x
y
36
32
40
28
posters
0
40
24
20
16
12
8
4
0
4
8
12
16
20 24 28
32 36 40
buttons
24
0
Should a line be drawn to connect
the intercepts? Think for a minute
to form an opinion.
This equation is in standard form. What can we learn by
looking at it in slope-intercept form?
5x  3y  120
+3
x
y
0
40
3
35
3y   5x  120
-5
3y
3

y 
5
3
5
3
Look for this pattern in
the table of values. The
change in y is down 5;
the change in x is up 3.
x
12 0
3
x  40
y-intercept
+3
y
0
40
3
35
6
30
9
25
12 20
15 15
18 10
21
5
24
0
36
32
-5
28
posters
x
40
24
20
16
12
8
4
0
4
8
12
16
20 24 28
32 36 40
buttons
The slope you just found shows how
the change in y and the change in x
can help to find other possible
combinations of buttons and posters.
Dogs sell for $40 and cats sell for $35 at Pets-R-Us. Sales
figures for the busy holiday shopping season showed that
the store received $840 total for dog and cat sales in one
weekend. Write an equation to describe the sales that
weekend of dogs, x, and cats, y.
Let x = # dogs
Let 40x = VALUE of dogs
Let y = # cats
Let 35y = VALUE of cats
Value of dogs
+
40x
+
35y
8x
+
7y
Value of cats
=
Total Cost
= 840
= 168
+7
x
y
0
24
7
16
14
8
21
0
No! Who wants
half a dog or
two- thirds of a
cat?
30
27
-8
24
21
Should the xand y-intercepts
be connected in
this case?
18
15
12
9
6
3
0
3
6
9
12 15
18 21
24 27 30
Put the equation in
slope-intercept form.
8
Using the slope information, find
y   x  24
7
more combinations of dogs and cats.