Lines so Far

Lines so far

The Rule y=mx+c

• m= gradient

• c = y-intercept

Gradient

• rise = 2

• run= 2

• m=rise/run

• m=2/2

• m=1

y-intercept (c)

• point where the line cuts the y-axis

• y-intercept = (0,2)

• c=+2

• 
  

• 
  

Put it together

• m=1

• c=+2

• y=mx+c

• y=x+2

Multiple Choice

What is the gradient

• m=2

• m=1

• $m=\frac{1}{2}$

• m=-2

Multiple Choice

What is the y-intercept

• $c=3$

• $c=-3$

• $c=0$

• $c=1$

Multiple Choice

Put it together. What is the rule

• $y=-2x+3$

• $y=2x-3$

• $y=-2x-3$

• $y=-3x+2$

Multiple Choice

What is the rule

• $y=-2x+3$

• $y=2x+3$

• $y=\frac{1}{2}x+3$

• $y=-\frac{1}{2}x+3$

Rule from a Table

• m=change in y/change in x

• c is added to make the y value

Gradient (m)

• change in y =+2

• change in x = +1

• m=2/1

• m=2

Use the point (1,5)

• m=2

• y=mx+c

• 5=2(1)+c

• 5=2+3

• c=+3

Put it together:

• m=2

• c=+3

• y=mx+c

• y=2x+3

• 
  

Multiple Choice

What is the gradient?

• $m=\frac{1}{3}$

• $m=3$

• m = 7

• m=-3

Multiple Choice

Using the point (1,4) with m=3 for the rule y=mx+c what is c?

• c = 1

• c=3

• $c=-1$

• c = 4

Multiple Choice

If m=3 and c=+1 what is the rule

• y=x+3

• y=3x+1

• y=3x -1

• y=x-3

Multiple Choice

What is the rule?

•  $y=\frac{1}{2}x+8$  

•  $y=-\frac{1}{2}x+8$  

•  $y=-\frac{1}{2}x+7$  

•  $y=-\frac{1}{2}x+9$  

Given a rule check the points agree

• the y value is found by using the rule on the x value

• a rule y=2x+3

• multiply x by 2 then +3

• If x =5

• y=2 x 5 +3

• y=13

• (5,13) lies on the line with the rule y=2x+3

Rule $y=-2x+4$   

• Does (3,8) lie on the line 

•  $y=-2\times3+4$  

•  $y=-2$  

•  $\left(3,-2\right)$  agrees with the rule

•  $\left(3,8\right)\$  does not agree with the rule

• (3,8) does not lie on the line

• 
  

Multiple Choice

Does (2,9) lie on the line  $y=2x+7$  ?

• Yes 

• No (2,11) lies on the line

• No (2, 10) lies on the line

Multiple Choice

 $y=5x-9$  Does (2,1) lie on the line

• Yes 

• No 

• No (2,9) lies on the line

Multiple Choice

 $y=-2x+4$  Which point lies on the line

•  $\left(-2,4\right)$  

•  $\left(2,0\right)$  

•  $\left(1,4\right)$  

•  $\left(0,-4\right)$