Question

5)

x	y
-2	-6
0	-4
1	-2
2	0
3	2

slope:
y intercept:
6)

x	y
-2	10
0	4
3	-5
6	-14
8	-20

slope :
y intercept:

1. question from the regents, june 2021what ordered pair does not fall on the line formed by the other three?

\ta. (16,18)\t\tc. (9,10)
\tb. (12,12)\t\td. (3,6)

Explanation:

For Problem 5:

Step1: Pick two points for slope

Use points $(0, -4)$ and $(1, -2)$

Step2: Calculate slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-2 - (-4)}{1 - 0}=\frac{2}{1}=2$

Step3: Identify y-intercept

Y-intercept is $y$ when $x=0$, from table $b=-4$

Step1: Pick two points for slope

Use points $(0, 4)$ and $(2, 10)$

Step2: Calculate slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{10 - 4}{2 - 0}=\frac{6}{2}=3$

Step3: Identify y-intercept

Y-intercept is $y$ when $x=0$, from table $b=4$

First, find the linear relationship between $x$ and $y$ for the valid points. Calculate the slope between pairs:

• Between $(3,6)$ and $(12,12)$: $m=\frac{12-6}{12-3}=\frac{6}{9}=\frac{2}{3}$
• Between $(3,6)$ and $(9,10)$: $m=\frac{10-6}{9-3}=\frac{4}{6}=\frac{2}{3}$
• Between $(3,6)$ and $(16,18)$: $m=\frac{18-6}{16-3}=\frac{12}{13}

eq\frac{2}{3}$
The line equation is $y=\frac{2}{3}x + 4$. Substitute $(16,18)$: $y=\frac{2}{3}(16)+4=\frac{32}{3}+4=\frac{44}{3}\approx14.67
eq18$, so it does not lie on the line.

Answer:

Slope: $2$
Y intercept: $-4$

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For Problem 6: