Error: The student switched m and b. Correct Graph:
Practice makes perfect
To determine the error(s), let's begin by analyzing the given equation. Then we can draw the correct graph.
Equation
Let's start by recalling the slope-intercept form of a line.
y= mx+ bIn the above formula, m is the slope and b is the y-intercept. Let's now write the given equation.
y= - 2x+ 1
We can see that the slope is - 2. This means that to get from one point on the line to another, we should move 2 units down and 1 unit to the right. We can also see that the y-intercept is 1. The graph should cross the y-axis at the point (0,1).
Graph
Now, let's take a look at the drawn graph.
From the marked points on the graph, we can see that the y-intercept is (0,-2). Additionally, to move from this to another point on the line, we move 1 unit up and 1 unit to the right. This means the slope is 11=1. Let's summarize this information and the one obtained from the equation.
Equation
Graph
Slope
- 2
1
y-intercept
1
- 2
We can conclude that the student who attempted to graph the function from the given equation switched the slope and the y-intercept. They graphed the function using m as the y-intercept and b as the slope. We will graph the equation correctly, knowing that the y-intercept is 1, and that the slope is - 2.
