1. 5-3 Standard Form
Hubarth
Algebra

2. Standard Form of a Linear Equation
The standard form of a linear equation is Ax + By = C, where A, B and C are real numbers,
and A and B are not both 0.
Ex 1 Finding x- and y- Intercepts
Find the x- and y-intercepts of 2x + 5y = 6.
Step 1  To find the x-intercept, substitute 0 for y and
solve for x.
Step To find the y-intercept,
substitute 0 for x and
solve for y.
2x + 5y = 6
2x + 5y = 6
2x + 5(0) = 6
2(0) + 5y = 6.
5y = 6
2x = 6
y = 6 5
x = 3
The y-intercept is . 6 5
The x-intercept is 3.

3. Ex 2 Graphing Lines Using Intercepts
Graph 3x + 5y = 15 using intercepts.
Step 1  Find the intercepts.
3x + 5y = 15
3x + 5(0) = 15 Substitute 0 for y.
3x = 15 Solve for x.
x = 5
3(0) + 5y = 15 Substitute 0 for x.
5y = 15 Solve for y.
y = 3
Step 2  Plot (5, 0) and (0, 3).
Draw a line through the points.

4. Ex 3 Graphing Horizontal and Vertical Lines
a. Graph y = 4
b. Graph x = –3.
0 • x + 1 • y = 4 Write in standard form.
For all values of x, y = 4.
1 • x + 0 • y = –3 Write in standard form.
For all values of y, x = –3.

5. Ex 4 Transforming To Standard Form
Write y = x + 6 in standard form using integers. 2 3
y = x + 6 2 3 2 3
(3)y = (3) x + 6(3) Multiply every term by 3.
3y = 2x Use the Distributive Property.
–2x + 3y = Subtract 2x from each side.
The equation in standard form is –2x + 3y = 18.

6. . . Practice 1. Find the x- and y-intercepts of 2x + 3y = 6.
x-int = (3, 0)
y-int = (0, 2)
2. Graph 4x + 2y = -8 using the x- and y- intercepts.
x-int = (-2, 0)
y-int = (0, -4) . .
3. What type of line does the graph of each equation form.
a. x = 3 b. y = -6
vertical line
horizontal line
2x + 5y = 5