Question

topic 2 review
which of the following equations represents the following blue line? * 1 point
graph of a line with points p, q, r
options:

• y = x - 0.5
• y = 2x + 1 (selected)
• y = x + 1
• x = 1 - y

a lake near the arctic circle is covered by sheet of ice during the cold * 1 point

Explanation:

Step1: Recall slope-intercept form

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

Step2: Find the y - intercept ($b$)

From the graph, the line crosses the y - axis at $(0,1)$, so $b = 1$.

Step3: Calculate the slope ($m$)

We can use two points on the line, for example, $P(0,1)$ and $R(1,4)$? Wait, no, let's take $P(0,1)$ and $Q(- 2,-3)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(-2,-3)$. Then $m=\frac{-3 - 1}{-2-0}=\frac{-4}{-2} = 2$.

Step4: Write the equation

Using $y=mx + b$ with $m = 2$ and $b = 1$, we get $y=2x + 1$. We can also check the other points. For $x = 1$, $y=2(1)+1=3$? Wait, the point $R$ in the graph seems to be at $(1,4)$? Wait, maybe I misread the point. Wait, if $x = 1$, for $y = 2x+1$, $y=3$? Wait, no, maybe the point $R$ is at $(1,3)$? Wait, the grid: when $x = 1$, the y - coordinate for the line: from the graph, the line passes through $(0,1)$ and when $x = 1$, let's see the rise over run. From $(0,1)$ to $(1,3)$? Wait, no, the slope is 2, so from $(0,1)$, moving 1 unit right (x increases by 1) and 2 units up (y increases by 2), so $y=1 + 2(1)=3$. Maybe the point $R$ is at $(1,3)$. Anyway, the equation $y = 2x+1$ has a slope of 2 and y - intercept 1, which matches the graph.

Answer:

B. $y = 2x + 1$ (assuming the options are labeled as A: $y=x - 0.5$, B: $y = 2x+1$, C: $y=x + 1$, D: $x = 1 - y$)