Section 5.6 ­ The Standard Form of a Linear Equation
Equations of Lines
slope­intercept form
y = mx + b
point­slope form
y ­ y1 = m(x ­ x1)
vertical line x = a
horizontal line
y = b
standard form
Ax + By = C
A, B, and C are real numbers
A and B are not both zero
Examples:
Write each equation in standard form.
1. ­5x + 11 = 1 y
2
2. x + 3y ­ 4 = 0
3. 0.3x ­ 0.4y = 7.5
4. (­5, 1) , m = 3
4
5. (3, 0) and (­5, 3)
6. (­4, 1) and (2, ­5)
7. a horizontal line through (6, ­5)
8. a vertical line through (­2, ­7)
9. You are starting a garden and want to plant marigolds and zinnias. Marigold plants cost $1.50 each while zinnia plants cost $2.50 each. You have $15 to spend. Write a linear model for the possible combinations of marigold zinnia plants. How many zinnia plants can you buy if you buy 5 marigold plants?