Graphing Using Slope Intercept Form Hopefully you remember
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. 2 x – y = -3 -2 x -y = -2 x – 3 y = 2 x + 3 3. -5 x – 3 y = 15 +5 x -3 y = 5 x + 15 2. 4 x + 2 y = 6 -4 x 2 y = -4 x + 6 y = -2 x + 3 4. 4 x + 3 y = 24 -4 x 3 y = -4 x + 24
Now let’s look at each equation and decide what the slope and y-intercept is. y = mx + b 1. y = -3 x + 6 m= b = (0, 6) 3. y = -x m= b = (0, 0) 5. x + 3 y = 9 m= b = (0, 3) 2. y = 2 x – 5 m= b = (0, -5) 4. 2 y = 8 x +10 y = 4 x + 5 m= b = (0, 5) m= b = (0, -8) 6. x – 2 y = 16
EVERYBODY GET A COMMUNICATOR!!
Now we can finally graph using slope-intercept form. y = -3 x + 2 m= b = (0, 2) y = mx + b
Graph using slope-intercept y = mx + b form. x+y=0 y = -x m= b = (0, 0)
Graph using slope-intercept 3 x - 3 y = 9 form. -3 x -3 y = -3 x + 9 -3 -3 -3 y=x-3 m= b = (0, -3)
Graph using slope-intercept 4 x + 5 y = 15 form. -4 x 5 y = -4 x + 15 5 m= b = (0, 3)
Graph using slope-intercept 4 x - y – 3 = 0 form. -4 x - y – 3 = -4 x +3 +3 -y = -4 x + 3 m= b = (0, -3)
Graph using slope-intercept 2 x - 3 y – 6 = 0 form. -2 x -3 y – 6 = -2 x +6 +6 -3 y = -2 x + 6 -3 -3 -3 m= b = (0, -2)
Graph using slope-intercept x–y+4 =0 form. -x -x -y + 4 = -x -4 -4 -y = -x - 4 -1 -1 -1 m= b = (0, 4)
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 + 2 y = 6 b. ) -x + 2 y = -2 +x +x 2 y = x + 6 y = mx + b 2 y = x - 2 2 2 2 c. ) x + 2 y = 4 -x -x 2 y = -x + 4 2 2 2 “a” and “b” are parallel
For each problem, tell me if the two equations are parallel. y = mx + b 1. y = -3 x + 2 y = -3 x - 4 Yes!!!!! y + 3 x = -4 2. 2 x – 12 = y y = 2 x - 12 Yes!!!!! y = 10 + 2 x y = 2 x + 10 3. y = x + 8 Yes!!!!! x – y = -1 y=x+1 4. 2 x – 5 y = -3 No!!!! 5 x + 2 y = 6
Write the equation of a line that has a yintercept of -3 and a slope of -4. 1. y = -3 x – 4 2. y = -4 x – 3 3. y = -3 x + 4 4. y = -4 x + 3
Write an equation of the line that goes through the points (0, 1) and (1, 4). 1. y = 3 x + 4 2. y = 3 x + 1 3. y = -3 x + 4 4. y = -3 x + 1
Find the slope and y-intercept. 4) 5 x - 3 y = 6 Write it in slope-intercept form. (y = mx + b) 5 x – 3 y = 6 -3 y = -5 x + 6 -3 -3 -3 m= y= x-2 b = -2
Find the slope and y-intercept. 5) 2 y + 2 = 4 x Write it in slope-intercept form. (y = mx + b) 2 y + 2 = 4 x 2 y = 4 x - 2 2 y = 2 x - 1 m=2 b = -1
Find the error in the problem, explain your reasoning.
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