Question

write the equation for a line with a slope of -2 and a y - intercept of 3 in the box to the right.
what are the slope and y - intercept for the linear function represented in the table to the right?
how do you know?
write your answer in the box below.
(table with x values: -2, -1, 0, 1, 2 and corresponding y values: 3, 5, 7, 9, 11)

Explanation:

Step1: Use slope-intercept form

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step2: Substitute given values

Substitute $m=-2$ and $b=3$ into the formula:
$y = -2x + 3$

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Step1: Calculate slope from table

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(-1,5)$:
$m=\frac{5-3}{-1-(-2)}=\frac{2}{1}=2$

Step2: Find y-intercept from table

The y-intercept is the $y$-value when $x=0$. From the table, when $x=0$, $y=7$, so $b=7$.

Step3: Verify consistency

Check with another pair: $(0,7)$ and $(1,9)$: $m=\frac{9-7}{1-0}=2$, confirming slope. The pattern of $y$ increasing by 2 when $x$ increases by 1 holds for all pairs, so the linear function has slope 2 and y-intercept 7.

Answer:

1. $y = -2x + 3$
2. Slope: $2$, y-intercept: $7$; The slope is constant ($\frac{\Delta y}{\Delta x}=2$) across all x-y pairs, and the y-intercept is the y-value when $x=0$.