2.3 Graph Equations of Lines

In this lesson you will: Use the slope intercept form of a linear equation to graph linear equations. Use the standard form of a linear equation to graph linear equations.

It gives us a way to locate points (or sets of points) in the plane. Remember the Cartesian Coordinate system? It is also sometimes called The Rectangular Coordinate System. y-axis 10 Quadrant II 8 Quadrant I 6 4 Origin 2 -10 -8 -6 -4 -2 O 2 4 6 8 10 x-axis -2 -4 Quadrant III Quadrant IV y-coordinate -6 -8 (10,-8) x-coordinate It gives us a way to locate points (or sets of points) in the plane.

Slope-Intercept Form If the graph of the equation “crosses the y-axis” at the point (0,3), we say the y-intercept is 3. If the graph intersects the y-axis at the point (0,b) we say the y-intercept is b. To find the y-intercept of a line, let x = 0 and solve for y. The slope intercept form of a linear equation y = mx + b has slope m and y-intercept b. Notice the line to the right has an x-intercept of (-2,0).

Graph the line First, locate the y-intercept -2. From that point, move 3 units up (change in y) and then 4 units right (change in x). Draw the line.

In addition to the slope-intercept form for the equation of a line, there are other forms too.

Forms of a Linear Equation Standard Form: Ax + By = C, Where A, B, and C are real numbers and A and B are not both zero. Find the values A, B, and C for the next linear equations: 4x + 3y = 6 2x = 7y -1 .75y – 2x = 1 -7y -7y y – 2x = 1 3 4 A= 4 (4) A= 2 B= 3 2x – 7y = -1 B= -7 C= 6 3y – 8x = 4 C= -1 (-1) -8x + 3y = 4 3x - 6y = 5 x + y = 2 1 4 3 8x -3y = -4 A= 3 A= 8 x + y = 2 1 4 3 B= -6 (4) B= -3 C= 5 C= -4 3x + y = 8 A= 3 B= 1 C= 8

Find the x-intercept and y-intercept of the following equation and use the intercepts to graph it: 4x + 2y = 8 y- intercept: x- intercept: 4 2 6 -2 -4 -6 8 10 -8 -10 x y Let’s make x= 0; Let’s make y= 0; 4( ) + 2y = 8 4x+ 2( ) = 8 4x = 8 (0, 4) 2y = 8 4 4 2 2 (2,0) x = 2 y = 4 (0, 4) (2,0)

Find the x-intercept and y-intercept of the following standard form equation and use the intercepts to graph it: 6x - 3y = 18 y- intercept: x- intercept: 4 2 6 -2 -4 -6 8 10 -8 -10 x y Let x= 0; Let y= 0; 6( ) - 3y = 18 6x -3( ) = 18 6x = 18 -3y = 18 6 6 -3 -3 (3,0) x = 3 y = -6 (0, -6) (3,0) (0, -6)

Change the equation to standard form then find the x-intercept and y-intercept and use the intercepts to graph it: y - x = 1 1 5 y - x = 1 1 5 (5) 4 2 6 -2 -4 -6 8 10 -8 -10 x y (-1) y – 5x = 5 5x – y = -5 (0, 5) y- intercept: x- intercept: (-1,0) Let’s make x= 0; Let’s make y= 0; 5( ) - y = -5 5x - ( ) = -5 5x = -5 - y = -5 5 5 -1 -1 x = -1 y = 5 (0, 5) (-1,0)

Finally, notice The equation of Horizontal lines have the form y = c The equation of Vertical lines have the form x = c. y = 4 x = -3