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# Slope-Intercept Form

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#### Transcript of Slope-Intercept Form

If a line has a slope m and the y-intercept is b, then the line is described by the equation: SLOPE-INTERCEPT FORM slope=2

y-intercept: (0,5) Slope-Intercept Form Review y=mx+b slope y-intercept

(0,b) m=2

b=5 y=mx+b y=2x+5 slope=-1/3

y-intercept: (0,-3) m=-1/3

b=-3 y=mx+b y=-1/3x+(-3) y=-1/3x-3 slope=-3

y-intercept: (0,2) y=mx+b slope y-intercept

(0,b) slope=4

through (2,5) y=mx+b slope=4

through (2,5) m=4

x=2

y=5 y=mx+b m=4

x=2

y=5 5=4(2)+b 5=4(2)+b

5= 8 + b

-8 -8

-3=b y=mx+b m=4

b=-3 y=4x-3 slope=8

through (-3,1) y=mx+b

1=8(-3)+b

1 =-24+b

+24 +24 25=b Now that you have found b, plug it back to the standard form with the provided m.

y=mx+b

y=8x+25 Use slope-Intercept Form to Graph y=4x-3 slope

4 y-intercept

(0,-3) 1 m 1 y=(-1/2)x+5 2y - 8x = 20

+8x +8x

2y = 20 + 8x

2 2 2

y = 10 + 4x

y = 4x + 10 You always want to rewrite your equation in slope intercept form y=mx+b. y=mx+b 1. add 8x to each side

2. divide each side by 2

3. rewrite in slope intercept form Application To rent a van, a moving company charges $30.00 plus $0.50 per mile. y=mx+b Write an equation in slope intercept form for the line that passes through the points (-1,-9) and (2,6) y=mx+b m= y y - x - x = 6-(-9) 2-(-1) = 15 3 = 5 1. Find the slope 2. Choose one of the points provided and plug it into the slope-intercept form along with m (2,6)

m=5

x=2

y=6 y=mx+b

6=5(2)+b 3. Solve for b 6 = 5(2)+b

6 = 10+b

-10 -10 -4=b 4. Plug m and b back in the slope intercept form y=5x-4 Write an equation in slope intercept form for the line that passes through the points (8,-2) and (4,1) y=mx+b m= y y - x - x = = 1. Find the slope 2. Choose one of the points provided and plug it into the slope-intercept form along with m ( , )

m=

x=

y= y=mx+b 3. Solve for b =b 4. Plug m and b back in the slope intercept form y= x+ starting value rate of change m=0.5

b=30 y=0.5x+30 a) write an equation that represents the cost of a function of the number of miles. y represents the cost. x represents the number of miles. b) Find the cost of the van for 150 miles y=0.5x+30

y=0.5(150)+30

y=105 The cost of the van for 150 miles is $105. Write an equation in slope intercept form given a slop and y-intercept Write an equation in slope-intercept form given a slope and a point. Write an equation in slope-intercept form given two points. m>o: the slope is positive

m<0: the slope is negative

Full transcripty-intercept: (0,5) Slope-Intercept Form Review y=mx+b slope y-intercept

(0,b) m=2

b=5 y=mx+b y=2x+5 slope=-1/3

y-intercept: (0,-3) m=-1/3

b=-3 y=mx+b y=-1/3x+(-3) y=-1/3x-3 slope=-3

y-intercept: (0,2) y=mx+b slope y-intercept

(0,b) slope=4

through (2,5) y=mx+b slope=4

through (2,5) m=4

x=2

y=5 y=mx+b m=4

x=2

y=5 5=4(2)+b 5=4(2)+b

5= 8 + b

-8 -8

-3=b y=mx+b m=4

b=-3 y=4x-3 slope=8

through (-3,1) y=mx+b

1=8(-3)+b

1 =-24+b

+24 +24 25=b Now that you have found b, plug it back to the standard form with the provided m.

y=mx+b

y=8x+25 Use slope-Intercept Form to Graph y=4x-3 slope

4 y-intercept

(0,-3) 1 m 1 y=(-1/2)x+5 2y - 8x = 20

+8x +8x

2y = 20 + 8x

2 2 2

y = 10 + 4x

y = 4x + 10 You always want to rewrite your equation in slope intercept form y=mx+b. y=mx+b 1. add 8x to each side

2. divide each side by 2

3. rewrite in slope intercept form Application To rent a van, a moving company charges $30.00 plus $0.50 per mile. y=mx+b Write an equation in slope intercept form for the line that passes through the points (-1,-9) and (2,6) y=mx+b m= y y - x - x = 6-(-9) 2-(-1) = 15 3 = 5 1. Find the slope 2. Choose one of the points provided and plug it into the slope-intercept form along with m (2,6)

m=5

x=2

y=6 y=mx+b

6=5(2)+b 3. Solve for b 6 = 5(2)+b

6 = 10+b

-10 -10 -4=b 4. Plug m and b back in the slope intercept form y=5x-4 Write an equation in slope intercept form for the line that passes through the points (8,-2) and (4,1) y=mx+b m= y y - x - x = = 1. Find the slope 2. Choose one of the points provided and plug it into the slope-intercept form along with m ( , )

m=

x=

y= y=mx+b 3. Solve for b =b 4. Plug m and b back in the slope intercept form y= x+ starting value rate of change m=0.5

b=30 y=0.5x+30 a) write an equation that represents the cost of a function of the number of miles. y represents the cost. x represents the number of miles. b) Find the cost of the van for 150 miles y=0.5x+30

y=0.5(150)+30

y=105 The cost of the van for 150 miles is $105. Write an equation in slope intercept form given a slop and y-intercept Write an equation in slope-intercept form given a slope and a point. Write an equation in slope-intercept form given two points. m>o: the slope is positive

m<0: the slope is negative