# 4.7 graphing using slope-intercept form

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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. - PowerPoint PPT PresentationTRANSCRIPT

4.7 Graphing Using Slope Intercept Form

4.7 Graphing Using Slope-Intercept FormHopefully you remember from last section, that we can graph a line easily when given:1. a random point2. the slope of the lineLets do an example of this:

Point (2,3)

Slope = 2

Wouldnt it be great if we could just look at an equation and figure out its slope and a point???!!! WE CAN!!! YAHHHH!!!!

BY USING SLOPE-INTERCEPT FORMSLOPE-INTERCEPT FORM

EXAMPLE #1So all we have to do issolve 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

Lets practice converting an equation to slope-intercept form.In other words: SOLVE FOR y2x y = -3 2. 4x + 2y = 6

3. -5x 3y = 15 4. 4x + 3y = 24-2x -2x -y = -2x 3 y = 2x + 3-4x -4x 2y = -4x + 6 y = -2x + 3+5x +5x -3y = 5x + 15

-4x -4x 3y = -4x + 24

Now lets look at each equation and decide what the slope and y-intercept is.y = -3x + 6 2. y = 2x 5

3. y = -x 4. 2y = 8x +10

5. x + 3y = 9 6. x 2y = 16m = 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 + bEVERYBODY GET A COMMUNICATOR!!Now we can finally graph using slope-intercept form.y = -3x + 2m =

b = (0,2)

y = mx + bGraph using slope-intercept form.x + y = 0m =

b = (0,0)

y = -xy = mx + bGraph using slope-intercept form.3x - 3y = 9m =

b = (0,-3)

y = x - 3-3x -3x-3y = -3x + 9-3 -3 -3Graph using slope-intercept form.4x + 5y = 15m =

b = (0,3)

-4x -4x5y = -4x + 155 5 5Graph using slope-intercept form.4x - y 3 = 0m = b = (0,-3)

-4x -4x- y 3 = -4x +3 +3-y = -4x + 3Graph using slope-intercept form.2x - 3y 6 = 0m =

b = (0,-2)

-2x -2x-3y 6 = -2x +6 +6-3y = -2x + 6-3 -3 -3Graph using slope-intercept form.x y + 4 = 0m =

b = (0,4)

-y + 4 = -x -4 -4-y = -x - 4-1 -1 -1-x -xGraph using slope-intercept form.m =

b = (0,1)

Now I want you to graph these two equations on the same graphm =

b = (0,3)

m =

b = (0,-2)

THESE LINES ARE PARALLEL!!

THEY HAVE THE SAME SLOPEy = mx + bAre these lines parallel???a.) -x + 2y = 6 b.) -x + 2y = -2

c.) x + 2y = 4+x +x2y = x + 62 2 2

+x +x2y = x - 22 2 2

-x -x2y = -x + 42 2 2

a and b are parallely = mx + bFor each problem, tell me if the two equations are parallel.y = mx + b1. y = -3x + 2 y + 3x = -42. 2x 12 = y y = 10 + 2x3. y = x + 8 x y = -14. 2x 5y = -3 5x + 2y = 6y = -3x - 4Yes!!!!!y = 2x - 12y = 2x + 10Yes!!!!!y = x + 1Yes!!!!!

No!!!!Write the equation of a line that has a y-intercept of -3 and a slope of -4.y = -3x 4y = -4x 3y = -3x + 4y = -4x + 3Write an equation of the line that goes through the points (0, 1) and (1, 4).y = 3x + 4y = 3x + 1y = -3x + 4y = -3x + 1-3-3-3Find the slope and y-intercept.4)5x - 3y = 6Write it in slope-intercept form. (y = mx + b) 5x 3y = 6 -3y = -5x + 6

y = x - 2

m =

b = -2

Write it in slope-intercept form. (y = mx + b) 2y + 2 = 4x 2y = 4x - 2

y = 2x - 1Find the slope and y-intercept. 5) 2y + 2 = 4x222m = 2b = -1Find the slope and y-intercept of y = -2x + 4m = 2; b = 4m = 4; b = 2m = -2; b = 4m = 4; b = -2