The graph of line l is shown in the xy-plane.What is the slope of line l?

1. TRANSLATE the graph information

To find the slope of a line, you need the coordinates of two points that lie on that line.

• Identify two clear points on line l:

Looking at the graph carefully:

• The line crosses the y-axis at (0, 4)
• The line crosses the x-axis at (2, 0)

? Tip: Choose intercepts when possible—they're easy to read accurately because they lie exactly on the axes.

2. SIMPLIFY using the slope formula

Now that we have two points, we can use the slope formula:

\(\mathrm{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

• Let's assign our points:

• \(\mathrm{(x_1, y_1) = (0, 4)}\)
• \(\mathrm{(x_2, y_2) = (2, 0)}\)

• Substitute into the formula:

\(\mathrm{m = \frac{0 - 4}{2 - 0}}\)

\(\mathrm{m = \frac{-4}{2}}\)

\(\mathrm{m = -2}\)

⚠️ Watch those signs! The numerator is negative because we're subtracting a larger number from a smaller one (0 - 4 = -4).

Answer: -2

Alternative acceptable forms: -2, -2.0, -2/1

Why Students Usually Falter on This Problem

Most Common Error Path:

SIMPLIFY - Sign errors in calculation

Students correctly identify the points and set up the formula but make a sign error during calculation. Common mistakes:

• Calculating 0 - 4 = 4 (forgetting the negative)
• Getting confused with "negative divided by positive"
• Writing the answer as +2 instead of -2

The line clearly goes downward from left to right, which MUST mean a negative slope. If you get a positive answer, you know something went wrong.

This leads them to write +2 as their answer.

Second Most Common Error:

TRANSLATE - Misreading coordinates from the graph

Students might miscount grid lines or choose points that don't lie exactly on the line. For example:

• Reading the y-intercept as (0, 6) instead of (0, 4)
• Trying to use points like (-1, 5.something) where it's hard to read the exact y-value
• Confusing which coordinate is x and which is y

This leads to calculating an incorrect slope value like -3, -1, or other wrong numbers.

The Bottom Line:

This problem tests your ability to carefully read a graph and perform signed arithmetic. The concept is straightforward—slope is rise over run—but accuracy in reading coordinates and maintaining correct signs throughout the calculation are critical. Always double-check: Does your answer's sign match the direction of the line?