Question

purposeful practice
for points 1 through 4, find the slope and the y - intercept in the table.
1)

x	y
-1	2
0	-1
1	-4
2	-7

slope: ______________
y intercept : ______________
2)

x	y
-1	-5
0	-1
1	3
2	7

slope: ______________
y - intercept : ______________
3)

x	y
-1	3.5
0	3
1	2.5
2	2

slope: ______________
y - intercept: ______________
4)

x	y
-2	-17
0	-7
3	2.8
5	14

slope: ______________
y - intercept: ______________

Explanation:

Problem 1

Step1: Pick two points

Choose $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(-2,2)$

Step2: Calculate slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{2-5}{-2-(-3)}=\frac{-3}{1}=-3$

Step3: Find y-intercept

Use $y=mx+b$, substitute $m=-3$ and $(-3,5)$:
$5=-3(-3)+b \implies 5=9+b \implies b=5-9=-4$

Problem 2

Step1: Pick two points

Choose $(x_1,y_1)=(-2,-4)$ and $(x_2,y_2)=(-1,-1)$

Step2: Calculate slope

$m=\frac{-1-(-4)}{-1-(-2)}=\frac{3}{1}=3$

Step3: Find y-intercept

Substitute $m=3$ and $(-2,-4)$ into $y=mx+b$:
$-4=3(-2)+b \implies -4=-6+b \implies b=-4+6=2$

Problem 3

Step1: Pick two points

Choose $(x_1,y_1)=(-2,4)$ and $(x_2,y_2)=(-1,3.5)$

Step2: Calculate slope

$m=\frac{3.5-4}{-1-(-2)}=\frac{-0.5}{1}=-0.5$

Step3: Find y-intercept

Substitute $m=-0.5$ and $(-2,4)$ into $y=mx+b$:
$4=-0.5(-2)+b \implies 4=1+b \implies b=4-1=3$

Problem 4

Step1: Pick two points

Choose $(x_1,y_1)=(-3,-16)$ and $(x_2,y_2)=(-2,-8)$

Step2: Calculate slope

$m=\frac{-8-(-16)}{-2-(-3)}=\frac{8}{1}=8$

Step3: Find y-intercept

Substitute $m=8$ and $(-3,-16)$ into $y=mx+b$:
$-16=8(-3)+b \implies -16=-24+b \implies b=-16+24=8$

Answer:

1. Slope: $-3$, Y-intercept: $-4$
2. Slope: $3$, Y-intercept: $2$
3. Slope: $-0.5$, Y-intercept: $3$
4. Slope: $8$, Y-intercept: $8$