Find the slope of the line graphed below.

Answer first: I can’t determine the numeric slope because the graph itself wasn’t attached — please upload the graph image or tell me two clear points on the line (for example (x1,y1) and (x2,y2)). Meanwhile, here is exactly how to find the slope from a graphed line plus worked examples so you can finish this quickly once you give the graph.

Concept

The slope m of a line measures its steepness and is the ratio of the vertical change (“rise”) to the horizontal change (“run”) between any two distinct points on the line:
$$m=\frac{\text{change in }y}{\text{change in }x}=\frac{y_2-y_1}{x_2-x_1}.$$

Steps to find slope from a graph

1. Identify two points on the line that lie exactly at grid intersections (integer coordinates). Call them $(x_1,y_1)$ and $(x_2,y_2)$. Prefer points far apart to reduce reading error.
2. Compute the rise: $y_2-y_1$ (can be positive, negative, or zero).
3. Compute the run: $x_2-x_1$ (can be positive or negative, but do not swap order — keep matching points).
4. Compute the slope: $$m=\frac{y_2-y_1}{x_2-x_1}.$$ Simplify the fraction; keep the sign.
5. Interpret the sign: if $m>0$ the line rises left-to-right; if $m<0$ it falls left-to-right; if $m=0$ it’s horizontal; if undefined (division by zero) it’s a vertical line.

Two quick examples

Example A (positive slope):

• Points: $(1,2)$ and $(4,5)$.
• Rise: $5-2=3$. Run: $4-1=3$.
• Slope: $$m=\frac{3}{3}=1.$$

So the line has slope 1 (45° up-right).

Example B (negative slope):

• Points: $(-2,3)$ and $(2,-1)$.
• Rise: $-1-3=-4$. Run: $2-(-2)=4$.
• Slope: $$m=\frac{-4}{4}=-1.$$

So the line falls one unit for every one unit right.

Example C (vertical line):

• Points: $(3,-2)$ and $(3,5)$: run $=3-3=0$, so slope undefined (vertical line).

Common reading tips

• Always pick grid intersection points to avoid reading fractional coordinates.
• If the two points give a fraction like $\frac{2}{4}$ simplify to $\frac{1}{2}$.
• If you read coordinates in the wrong order you may get the same result as long as you pair consistently (i.e., subtract $y_1$ from $y_2$ and $x_1$ from $x_2$ with the same pairing).

What I need from you to give the exact numeric slope

• Upload the image of the graphed line, or
• Tell me two clear points on the line (e.g., (x1,y1) = (0,2) and (3,5)), or
• Tell me the y-intercept and another point, or describe the rise and run shown on the graph.

Summary: I can’t compute the numeric slope until I see the graph or two points. Upload the graph or give two points and I’ll compute the slope step-by-step and explain the result.