5.5 Standard Form:

Linear Equation: is an equation that models a linear function.

X-intercept: The point where the graph crosses the x-axis, ( y=0).

Y-intercept: The point where the graph crosses the y-axis, (x=0).

GOAL:

Whenever we are given a graph we must be able to provide the equation of the function in

Standard Form: The linear equation of the form:

Ax + By = Cwhere A, B and C are real whole numbers (no fractions) and A and B are not both zero.

EX: What are the x- and y-intercepts of the

graph of 5x – 6y = 60?

SOLUTION: There are many ways to find this information depending on the form you are given, but if you are given the standard form (Ax+By=C), then you must plug in zero for the other variable.

Finding the x-intercept: plug in zero for y

5x – 6y = 60 plug in y=05x – 6(0) = 605x = 60x = 60/5 12 (12,0) is the point.

Finding the y-intercept: plug in zero for x

5x – 6y = 60 plug in x=0

5(0) – 6y = 60– 6y = 60

(0, -10) is the pointy=60/-6 -10

Graph: 𝟓 𝒙−𝟔 𝒚=𝟔𝟎

X-intercept: (12, 0)

Y-intercept: ( 0, -10)

2

2

-2-2

YOU TRY IT: What are the x- and y-intercepts of the

graph of 3x + 4y = 24?

YOU TRY IT: (SOLUTION)Finding the x-intercept: plug in zero for y

3x + 4y = 24 plug in y=03x + 4(0) = 24

3x = 24

x = 24/3 8 (8,0) is the point.

Finding the y-intercept: plug in zero for x

3x + 4y = 24 plug in X=03(0) + 4y = 24

4y = 24

y = 24/4 6 (0,6) is the point.

Graph: 3

X-intercept: (8, 0)

Y-intercept: ( 0, 6)

Graphing Horizontal LinesRemember: x lines are vertical

y lines are Horizontal

X = 3

y = - 2

YOU TRY IT:

What are the graphs of x = -1 and y = 5

YOU TRY IT: (SOLUTION)Remember: x lines are vertical

y lines are Horizontal

X = -1

y = 5

TRANSFORMING TO STANDARD FORM

If we are given an equation in slope-intercept from (y = mx +b), and the point-slope form (y – y1=m(x-x1)) we can rewrite the equations into standard form:

Ax + By = Cwhere A, B and C are real whole numbers (no fractions) and A and B are not both zero.

EX: What are the standard forms of

1) y = - x + 5 and 2) y – 2 = - (x + 6)

SOLUTION: 1) Using the slope-intercept from y = - x + 5

We must get rid of any fraction, no fractions allowed:

7y = - 3x + 35

Inverse of dividing by 7 y = - x + 5

Inverse subtraction 3x

7y + 3x= 35 Variables in order

3x + 7y = 35 Ax + By = C form.

Graph: 𝟑 𝒙+𝟕𝒚=𝟑𝟓X-intercept: (11.7, 0)

Y-intercept: (0, 5)Here we would use: y = - x + 5down 3,right 7

SOLUTION: 2)Using the point-slope from y-2 = - (x + 6)

We must first distribute the slope

3y - 6 = - x -6

Distribute - y -2 = - x - 2

Inverse of division by 3 (multiply everything by 3). 3y + X = -6 +6 Variables to left numbers to the right of equal sign.

x + 3y = 0 Ax + By = C form.

We must then get rid of fractions

Graph: 𝒙+𝟑 𝒚=𝟎X-intercept: (0, 0)

Y-intercept: (0, 0)

We now use

y = - x + 0

USING STANDARD FORM AS MODEL

In real-world situations we can write and use linear equations to obtain important information to help us find out what we

can do with the resources we have.

EX: In a video game, you earn 5 points for each jewel you find. You earn 2 points for each star you find. Write and graph an equation that represents the number of jewels and stars you must find to earn 250 points.What are three possible combinations of jewels and stars you can find that will earn you 250 points?

SOLUTION: In a video game, you earn 5 points for each

jewel you find. Let x = the jewels you find.

You earn 2 points for each star you find. Let y = the starts you find.

Write the equation for a total of 250 points:

5x + 2y = 250

Graph: 5

X-intercept: (50, 0)

Y-intercept: (0, 125)

Star

s

Jewels25 50 75 100

255075

100

125150175200225

250

125

Graph: Three points are:(0, 125)

0 Jewels, 125 Stars

Star

s

Jewels25 50 75 100

255075

100

125150175200225

250

125

(25, 62.5)25 Jewels, 62.5 Stars

(25, 63)25 Jewels, 62.5 Stars

VIDEOS: Graphs

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/point-slope-form/v/point-slope-and-standard-form

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/point-slope-form/v/linear-equations-in-standard-form

CLASSWORK:

Page 323-325

Problems: As many as needed to master the concept