Algebra 1 Section 6.4

Graphing Linear Equations We can make a table of ordered pairs. We can use the x- and y- intercepts. We can use the slope-intercept form of the line.

Writing a Linear Equation We can write the equation of a line if given the following information: slope and y-intercept slope and a point on the line

Writing a Linear Equation We can write the equation of a line if given the following information: two points on the line the graph of the line

Example 1 Given: slope: ⅔ y-intercept: (0, -5) 2 3 y = m x + -5 b y = x – 5 2 3

Example 2 Given: slope: 3 point: (1, 5) y = m x + b y = 3x + 2 5 = 3 (1) + b 5 = 3 + b b = 2

Example 4 Given: slope: 0 point: (1, -6) y = m x + b y = 0x – 6 y = -6 -6 = (1) + b -6 = 0 + b b = -6

Example 5 Strategy: First, find the slope m. Next, find b. Then, use m and b to write the equation in slope-intercept form. 5 3 – 14 3

Example 5 y = m x + b 5 3 – 14 3 y = x + The second point, (4, -2), can be used to check your work since it must be a solution to the equation.

Example 6 The strategy will remain the same as before. The slope of the line is undefined; therefore, the line must be vertical. x = 7

Example 7 Choose two convenient points from the graph. Use the slope formula to determine the estimated rate of growth. people year m = 500

Example 7 Use one of the points, (2010, 56,500), and the slope to find b. b = -948,500

Example 7 Use the slope and b to write the equation in slope- intercept form. y = 500x – 948,500

Example 7 Rewrite the equation showing population as a function of time. P(t) = 500t – 948,500

Models In Example 7, the function acts as a model of population growth. It may be useful for years close to the data, but making predictions for faraway times often causes errors.

Homework: pp. 252-255