Graphing Linear Functions 3 Forms of Linear Equations

Graphing Linear Functions

3 Forms of Linear Equations 1. Slope-Intercept Form • m = slope • b = y-intercept y = mx + b

3 Forms of Linear Equations 2. Point-Slope Form y-k = m(x–h) • m = slope • (h, k) = a point on the line

3 Forms of Linear Equations 3. Standard Form Ax + By = C • x-intercept (plug in zero for y) • y-intercept (plug in zero for x)

Some Notes about SLOPE • • • Slope describes how a line moves from left to right It is also called the rate of change (especially in word problems) It is positive when the line is going up (from left to right) It is negative when the line is going down (from left to right) It is zero for a horizontal line (y = #) It is undefined for a vertical line (x = #) • m=

Some Notes about INTERCEPTS • An INTERCEPT is a point where a graph crosses an axis (x or y). • The x-intercept is the point where the graph crosses the x-axis. • X-Intercept = (x, 0) *The y-value is zero. • The y-intercept is the point where the graph crosses the y-axis. • Y-Intercept = (0, y) * The x-value is zero. • Y-Intercept: The y-value is b when the equation is in slope-intercept form.

Graphing from Equations There a few ways to graph lines. • Creating and Using Tables • Using a point and the slope • Using two points (and straightedge)

Examples – Determine the slope and intercepts 1. y = 3 x– 5 2. y– 2 = -4(x+2) 3. 3 x – 2 y = 12

Example – Graph the function (tables) First, Make a Table by plugging in x-values to obtain y-values. Make Points (x, y)

Example – Graph the function

Example – Graph the function

Example – Graph the function

Example – Graph the function (special cases) Ask yourself… Where does y equal 4?

Example – Graph the function (special cases) Ask yourself… Where does x equal -5?