6-4 Standard Form

You will be learning 3 different forms (or formats) for writing linear equations.

• Slope-intercept form• Standard form• Point-slope form

Standard FormAx + By = C

A, B, & C are real numbers.Ex. 2x + 3y = 6

A can be zero Ex. 5y = 10B can be zero Ex. 6x = 12C can be zero Ex. 6x + 5y = 0

A and B cannot BOTH be zero.If they were, your equation would be 0 = C…doesn’t make sense!

When an equation is written in standard form, you can calculate the x-intercept and the y-intercept.The x-intercept tells where the line passes through the x-axis. The value of “y” at this point is zero.

To find the value of “x” at this point, just set “y” equal to zero.Ex. 4x + 2y = 8If I set y=0, I will find the x-intercept.4x + 2(0) = 84x = 8x = 2 So the x-intercept is 2

When an equation is written in standard form, you can identify the x-intercept and the y-intercept.The y-intercept tells where the lines passes through the y-axis. The value of “x” at this point is zero.

To find the value of “y” at this point, just set “x” equal to zero.Ex. 4x + 2y = 8If I set x=0, I will find the y-intercept.4(0)+ 2y = 82y = 8y= 4 So the y-intercept is 4

Ex. 4x + 2y = 8Set x = 04(0)+ 2y = 82y = 8y= 4 y-intercept is 4

set y=04x + 2(0) = 84x = 8x = 2 x-intercept is 2I can graph the line based on these two points.

Some word problems are easiest to solve using the standard form.

Example: Your school is sponsoring a ziti dinner to raise money for a field trip that costs $4000. You estimate the 200 adults and 250 children will attend. How much should the ticket prices be?

Let x be the adult price and y be the kid price.You know that you want to raise a total of $4000.We know how many adults & kids (& the variables for prices).If we add the adult & kid info, we can get the total.

# of adults * cost per adult + # of kids * cost per kids = total income

200x + 250y = 4000

So now you’re wondering…

How does this help me?

Let’s graph our equation 200x + 250y = 4000Set x = 0250y = 4000y = 16The y-intercept is 16

set y=0200x = 4000x = 20The x-intercept is 20

x is the price for adults and y is the price for kids…If I charge $16 per kid and $0 per adult, I will reach my goal! If I charge $20 per adult and $0 per kid, I will also reach my goal. The line formed by connecting the points represents ALL other possible price combinations that will allow me to reach my goal!

Ziti Dinner

Adult Price

Kid

Pric

e