9 4 Slopeintercept form of Linear Equation Reviews

9. 4 Slope-intercept form of Linear Equation

Reviews of Previous Classes Equation: B=3 A

• the intersection of y-axis and the straight line • x=0, y=b • as ordered pair (0, b) y-intercept y=mx+b Speed (m/s) Slope 12 (0, 10) 10 v =-2 t+10 t=0, v=10 Speed (m/s) 8 6 4 2 0 0 1 2 3 4 Time (second) 5 6

Class 1 Example 2: The graph shows the total distance travelled in relation to the time spent to travel Distance Traveled Distance 2 (meter), D 2 5 10 15 20 25 30 D 1=3 t 35 30 25 Distance (meter) Time Distance 1 (second), t (meter), D 1 1 3 2 6 3 9 4 12 5 15 6 18 20 15 10 y=mx D 2=5 t D 3=100 t 5 0 0 1 2 3 4 Time (Second) 5 6 Tool Box 7

12 12 10 10 8 8 Speed (m/s) Speed 6 6 4 4 2 2 0 00 v =-2 t+10 1 0 2 Tool Box 1 3 4 2 5 6 time (s) 3 7 Time (second) 4 8 9 5 10 11 6 y=mx+b m= -2 v =-2 t+10 m=-2 v =-t+10 m=-1 v =-5 t+10 m=-5

y-intercept • the cross-point of yaxis and the straight line • x=0, y=b • as ordered pair (0, b) y=mx+b Slope Rate of Change • m>0, y-value increase, the greater m is, the faster y increase /the It measures(shows) how steeper the straight line • m=0, y is constant/does not fast y-value changes with change the changes of x-value • m<0, y-value decrease, the smaller m is, the faster y decrease /the steeper the straight line • m is undefined, x=constant

Desmos Play Time Create lines: y=x y=-x y=2 y=-2 x=-2 y=3 x+5 y=3 x-5 y=-3 x+5 y=-3 x -5

y (0, 10) b=10 slope m (x 1, y 1) x (x 1, y 1) and (x 2, y 2) are any two different points on the line (x 2, y 2) y=mx+b y=-2 x+10 (x 1, y 1) (2, 6) (x 2, y 2) (10, -10)

The rate of change between two points: y Run x Rise Determine the sign + or of slope!!!!!!

In summary: calculate slope m y (x 1, y 1) and (x 2, y 2) are any two different points on the line (x 1, y 1) OR x Rise Run (x 2, y 2) Count the divisions between two points Determine m is + or -

y Look for y-intercept: (0, 1) x

y Look for y-intercept: (0, 1) x 3 x

Look for y-intercept: (0, 1) y x