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2.3 Graph Equations of Lines Goal Graph linear equations in slope-intercept or standard form. Your Notes VOCABULARY Parent function The most basic function in a family of functions y-intercept The y coordinate of a point where the graph intersects the y - axis Slope-intercept form An equation of the form y= mx + b with slope m and y - intercept b Standard form of a linear equation The standard form of a linear equation is Ax + By= C where A and B are not both zero. x-intercept The coordinate of a point where a graph intersects the x – axis PARENT FUNCTION FOR LINEAR FUNCTIONS The parent function for the family of all linear functions is y = __x_. The graph of y = x is shown. In general, a y- intercept of a graph is the y - coordinate of a point where the graph intersects the y-axis. Your Notes USING SLOPE-INTERCEPT FORM TO GRAPH AN EQUATION Step 1 Write the equation in __slope-intercept__ form by solving for y. Step 2 __Identify__ the y-intercept b and use it to plot the point (0, b) where the line crosses the y -axis. Step 3 Identify the __slope__ m and use it to plot a second point on the line. Step 4 __Draw__ a line through the two points. Example 1 Graph an equation in slope-intercept form Graph y = 3 x + 1. 2 Step 1 The equation is already in slope-intercept form. Step 2 The y-intercept is __1__ , so plot the point (__0__,__1__) where the line crosses the__ y – axis__. 3 -3 ,so plot a second point on the line by starting at 2 Step 3 The slope is ______ or 2 (__0,1__) and then moving down _3_ units and right _2_ units. The second point is (__2,2__). Step 4 Draw a line through the two points. USING STANDARD FORM TO GRAPH AN EQUATION Step 1 Write the equation in standard form. Step 2 Identify the x-intercept by letting __y_ = 0 and solving for __x__. Use the xintercept to plot the point where the line crosses the x – axis. Step 3 Identify the y-intercept by letting __x__ = 0 and solving for __y__. Use the yintercept to plot the point where the line crosses the __y – axis__. Step 4 Draw a line through the two points. Your Notes Example 2 Graph an equation in standard form Graph 2x + 3y = 12. Solution Step 1 The equation is already in standard form. Step 2 2x + 3(__0__) = 12 Let y = __0__ x=6 Solve for x. Plot the x-intercept at (__6__,0). Step 3 2(__0__) + 3y = 12 Let x = __0__. y = __4__ Solve for y. Plot the y-intercept at (0,__4__). Step 4 Draw a line through the two points. HORIZONTAL AND VERTICAL LINES Horizontal lines The graph of y = c is the horizontal line through (__0__,__c__). Vertical lines The graph of x = c is the vertical line through (__c__,__0__). Example 3 Graph horizontal and vertical lines a. Graph y = 1 b. Graph x = 2. Solution a. The graph of y = 1 is the __horizontal__ line that passes through the point (0,_1__). Notice that every point on the line has a y-coordinate of 1_. b. The graph of x = 2 is the __vertical__ line that passes through the point (__2_,0). Notice that every point on the line has an x-coordinate of __2__. Your Notes Checkpoint Graph the equation. 1. y = 2x + 2 2. y = 4 x 4 3 3. 4x + 2y = 8 4. 5x + 3y = 15 5. y = 4 6. x = 2 Homework ______________________________________________________________________ ______________________________________________________________________