4.7 Graphing Using Slope-Intercept Form

Hopefully you remember from last section, that we can graph a line easily when given: 1. a random point 2. the slope of the line

Let’s do an example of this: Point (2,3) Slope = 2

Wouldn’t it be great if we could just look at an equation and figure out it’s slope and a point???!!! WE CAN!!! YAHHHH!!!! BY USING SLOPE-INTERCEPT FORM

SLOPE-INTERCEPT FORM EXAMPLE #1 So all we have to do is solve for “y” and we can see a slope and a point!!!

Some more examples… “b” is the y-intercept

So in order to use this form we must solve for “y”

Let’s practice converting an equation to slope-intercept form. In other words: SOLVE FOR “y” 1.2x – y = x + 2y = x – 3y = x + 3y = 24 -2x -y = -2x – 3 y = 2x x 2y = -4x + 6 y = -2x x -3y = 5x x 3y = -4x + 24

Now let’s look at each equation and decide what the slope and y-intercept is. 1.y = -3x y = 2x – 5 3. y = -x 4. 2y = 8x x + 3y = 9 6. x – 2y = 16 m = b = (0,6)m = b = (0,-5) m = b = (0,0) m = b = (0,5) m = b = (0,3)m = b = (0,-8) y = 4x + 5 y = mx + b

EVERYBODY GET A COMMUNICATOR!!

Now we can finally graph using slope-intercept form. y = -3x + 2 m = b = (0,2) y = mx + b

Graph using slope-intercept form. x + y = 0 m = b = (0,0) y = -x y = mx + b

Graph using slope-intercept form. 3x - 3y = 9 m = b = (0,-3) y = x x -3y = -3x

Graph using slope-intercept form. 4x + 5y = 15 m = b = (0,3) -4x 5y = -4x

Graph using slope-intercept form. 4x - y – 3 = 0 m = b = (0,-3) -4x - y – 3 = -4x y = -4x + 3

Graph using slope-intercept form. 2x - 3y – 6 = 0 m = b = (0,-2) -2x -3y – 6 = -2x y = -2x

Graph using slope-intercept form. x – y + 4 = 0 m = b = (0,4) -y + 4 = -x y = -x x

Graph using slope-intercept form. m = b = (0,1)

Now I want you to graph these two equations on the same graph m = b = (0,3) m = b = (0,-2) THESE LINES ARE PARALLEL!! THEY HAVE THE SAME SLOPE y = mx + b

Are these lines parallel??? a.) -x + 2y = 6 b.) -x + 2y = -2 c.) x + 2y = 4 +x 2y = x x 2y = x x 2y = -x “a” and “b” are parallel y = mx + b

For each problem, tell me if the two equations are parallel. y = mx + b 1. y = -3x + 2 y + 3x = x – 12 = y y = x 3. y = x + 8 x – y = x – 5y = -3 5x + 2y = 6 y = -3x - 4Yes!!!!! y = 2x - 12 y = 2x + 10 Yes!!!!! y = x + 1 Yes!!!!! No!!!!

Write the equation of a line that has a y- intercept of -3 and a slope of y = -3x – 4 2.y = -4x – 3 3.y = -3x y = -4x + 3

Write an equation of the line that goes through the points (0, 1) and (1, 4). 1.y = 3x y = 3x y = -3x y = -3x + 1

-3 Find the slope and y-intercept. 4)5x - 3y = 6 Write it in slope-intercept form. (y = mx + b) 5x – 3y = 6 5x – 3y = 6 -3y = -5x y = -5x + 6 y = x - 2 y = x - 2 m = b = -2

Write it in slope-intercept form. (y = mx + b) 2y + 2 = 4x 2y + 2 = 4x 2y = 4x - 2 2y = 4x - 2 y = 2x - 1 Find the slope and y-intercept. 5) 2y + 2 = 4x 2 22 m = 2 b = -1

Find the slope and y-intercept of y = -2x m = 2; b = 4 2.m = 4; b = 2 3.m = -2; b = 4 4.m = 4; b = -2