Question

name
writing slope intercept forms of equation based on graph
period
find the slope of each line.
1)
(0,2)
(1,-1)
slope (m) =
slope (m) =
y = mx + b
2)
y = mx + b
m = \frac{rise}{run}
sketch the graph of each line.

1. y = -x + 1
2. y = -2x + 1

m = -2

1. y = \frac{2}{3}x + 3

m = \frac{2}{3}

Explanation:

Step1: Find slope for line 1

Use points $(-3,2)$ and $(1,-1)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-1-2}{1-(-3)}=\frac{-3}{4}$

Step2: Find slope for line 2

Horizontal line, slope = 0.

Step3: Graph $y=-x+1$

1. y-intercept: $(0,1)$
2. Slope $m=-1$: from $(0,1)$, move 1 down, 1 right to $(1,0)$. Draw line through points.

Step4: Graph $y=-2x+1$

1. y-intercept: $(0,1)$
2. Slope $m=-2$: from $(0,1)$, move 2 down, 1 right to $(1,-1)$. Draw line through points.

Step5: Graph $y=\frac{2}{3}x+3$

1. y-intercept: $(0,3)$
2. Slope $m=\frac{2}{3}$: from $(0,3)$, move 2 up, 3 right to $(3,5)$. Draw line through points.

Answer:

1. Slope of line 1: $\boldsymbol{-\frac{3}{4}}$
2. Slope of line 2: $\boldsymbol{0}$
3. Graph for $y=-x+1$: Line through $(0,1)$ and $(1,0)$
4. Graph for $y=-2x+1$: Line through $(0,1)$ and $(1,-1)$
5. Graph for $y=\frac{2}{3}x+3$: Line through $(0,3)$ and $(3,5)$