Question

slope_ y intercept_
y = (1/2)x + 2
table with x and y values: x=-2 (y missing), x=-1 (y=1.5), x=0 (y=2), x=1 (y=2.5), x=2 (y=3)
graph
slope_ y intercept_
y = 2x - 1
table with x and y: x=-2 (y=-5), x=-1 (y=-3), x=0 (y=-1), x=1 (y=1), x=2 (y=3)
graph with handwritten notes
slope2 y intercept-1
y = ______
table with x and y: x=-5 (y=10), x=-4 (y=8), x=-3 (y=6), x=-2 (y=4), x=-1 (y=2)
graph
slope__ y intercept__

Explanation:

Step1: Find the slope

We use the formula for slope $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(-5, 10)$ and $(-4, 8)$. Then $m=\frac{8 - 10}{-4 - (-5)}=\frac{-2}{1}=-2$.

Step2: Find the y - intercept

The equation of a line is $y = mx + b$, where $b$ is the y - intercept. We can use one of the points, say $x=-1,y = 2$ and $m=-2$. Substitute into the equation: $2=-2\times(-1)+b$. So $2 = 2 + b$, which gives $b = 0$? Wait, no, let's check another point. Take $x = 0$ (we can find $x = 0$ by extending the pattern). When $x=0$, following the pattern (since slope is - 2, when $x$ increases by 1, $y$ decreases by 2. From $x=-1,y = 2$, when $x = 0$, $y=2-2 = 0$? Wait, but let's use the slope - intercept form properly. Let's use the point $(-1,2)$ and $m=-2$. $y=mx + b\Rightarrow2=-2\times(-1)+b\Rightarrow2 = 2 + b\Rightarrow b = 0$. Wait, but let's check with $x=-5,y = 10$: $y=-2x + b\Rightarrow10=-2\times(-5)+b\Rightarrow10 = 10 + b\Rightarrow b = 0$. So the y - intercept is 0. Wait, but let's check the pattern of the table. When $x=-5,y = 10$; $x=-4,y = 8$ (decrease by 2); $x=-3,y = 6$; $x=-2,y = 4$; $x=-1,y = 2$; so when $x = 0$, $y=0$. So slope is - 2 and y - intercept is 0.

Answer:

slope: $-2$, y - intercept: $0$