Standard Form of Equations and Lines

The slope-intercept form is one way to write the equation of a line. Another way is called standard form. The standard form looks like Ax + By = C.

Ax + By = C.

The standard form is useful for graphing vertical and horizontal lines.

Relate Standard Form to Horizontal and Vertical Lines

1. What does the graph of Ax +By = C look like when A = 0?

3y = -18

Solution:

The equation y = -6 does not include x, so x has no effect on the y-values.

The value of y is -6 for the x-value.

So, the graph of y = -6 is the horizontal line.

In the coordinate plane, an equation in one variable means that the other variable has no effect on the equation or the graph.

When A=0, the graph of Ax +By = C is a horizontal line.

2. What does the graph of Ax +By =C look like when B = 0?

Graph the linear equation 4x = 12.

Solution:

The value of x is 3 regardless of the value of y.

When B=0, the graph of the Ax + By = C is a vertical line.

Use the Standard Form of Linear Equation

The standard form for linear equations in two variables is Ax + By = C.

For example, 2x + 3y = 5 is a linear equation in standard form.

When an equation is given in this form, it’s pretty easy to find both intercepts (x and y).

Example 1:

Each CD in the store costs $10, and each book costs $ 6. If you want to spend exactly $32, write an equation in standard form modeling this situation. Let x represent the number of CDs you buy, and y represent the number of books you buy.

Find x-intercept of 10x + 6y =32.

x-intercept is ( 16 / 5, 0)

Find y-intercept of 10x + 6y =32.

y-intercept is (0, 16 / 3)

Graph the between points.

Example 2:

Lenin is running a concession stand at the basketball game. He sells hot dogs for $1 and sodas $0.50. At the end of the night, he made $200. Let x represent the number of hot dogs sold and y represent the number of sodas sold. Write an equation that can be used to find out how many hot dogs and how many sodas were sold.

Solution:

Exercise

1. How is the graph of the equation related to the standard form Ax + By =C?

1. Sketch the graph of the equation.
   1. 4x = 10
   2. – 9x = -27
   1. Write each equation in a standard form.
      1. y=4x -18
      2. y-1 = 2/3(x+6)

      

      1. Concert tickets cost $15 for general admission, but only $9 with a student ID. Ticket sales total $4500. Write and graph an equation that models this situation. How many student tickets were sold if 150 general admission tickets were sold?

      

      1. You have $30 to spend on downloading songs for your iPod. Company A charges $0.79 per song, and company B charges $0.99 per song. Write an equation that models this situation.
      2. Write equation for the below graph.

      

      1. How do we express the standard form of a linear equation?
      2. Graph the equation x= -6.
      3. In Ax + By =C.
         1. An and B are called _________.