Goal: Use slope-intercept form and standard form to graph equations.

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Presentation transcript:

Goal: Use slope-intercept form and standard form to graph equations.

Definitions y-intercept: the y-coordinate of a point where a graph intersects the y-axis. Slope-intercept form: y = mx+b m = slope b = y-intercept

Graphing Equations in Slope-Intercept Form Step 1: Write the equation in slope-intercept form by solving for y. Step 2: Find the y-intercept and plot the corresponding point. Step 3: Find the slope and use it to plot a second point on the line. Step 4: Draw a line through the two points.

Example 1: Graph y – ¾ x = 2 Write the equation in slope-intercept form by solving for y.

Checkpoint: Use slope Intercept form to graph lines 1. y = ½ x2. y = -x – 23. y –3 = 2/3 x

Standard Form x-intercept: the x-coordinate of a point where a graph intersects the x-axis. Standard Form: Ax+By=C where A and B are not both zero

Graphing Equations in Standard Form Step 1: Write the equation in standard form Step 2: Find the x-intercept) by letting y = 0 and solving for x. Plot the corresponding point. Step 3: Find the y-intercept by letting x = 0 and solving for y. Plot the corresponding point. Step 4: Draw a line through the two points.

Checkpoint – Draw Quick Graphs Graph the equation. Choose either method. 1. x + y = 7 2. y = - ½ x x + 2y = 10

Parallel and Perpendicular Lines Parallel Lines They lie in the same plane and never intersect Lines are parallel if and only if they have the same slope Perpendicular Lines They intersect to form a right angle. Lines are perpendicular if and only if their slopes are negative reciprocals of each other

Example 3: Graph Parallel and Perpendicular Lines a. Draw a graph of y = 3x + 4 b. Graph the line that passes through (0, -1) and is parallel to the graph of y = 3x + 4 c. Graph the line that is perpendicular to the graph of y = 3x + 4 at its y-intercept