Graphing Lines Worksheets - 15 Worksheets Library - Free Printable

Let’s solve each problem one by one. We’ll look at the equation and match it to the correct graph by checking two things:
1. The slope (how steep the line is and whether it goes up or down).
2. The y-intercept (where the line crosses the y-axis — that’s when x = 0).

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Problem 1: y = x + 1

This is in slope-intercept form: y = mx + b
→ m (slope) = 1 → for every 1 unit right, go up 1 unit.
→ b (y-intercept) = 1 → line crosses y-axis at (0, 1)

Look at the graphs:

- Graph (i): Goes down → wrong slope sign.
- Graph (ii): Crosses y-axis at -1 → wrong intercept.
- Graph (iii): Crosses y-axis at 1? Let’s check — yes, looks like (0,1), and goes up 1 for every 1 right → matches!
- Graph (iv): Crosses at -1 → no.

✔ So, answer for #1 is (iii)

Wait — let me double-check graph (iii) in problem 1. In the first row, third graph: starts at (0,1), goes through (1,2), (-1,0) — yes, that’s y = x + 1.

But wait — looking again at the options labeled under problem 1: they are labeled (i), (ii), (iii), (iv) below each graph.

Actually, in problem 1, the four graphs are labeled underneath as (i), (ii), (iii), (iv). Let’s recheck:

Graph (i): line going down from left to right → negative slope → not y=x+1.

Graph (ii): passes through (0,-1) and (1,0) → that’s y = x - 1 → not our equation.

Graph (iii): passes through (0,1) and (1,2) → yes! That’s y = x + 1.

Graph (iv): passes through (0,-1) and (1,0) → same as (ii)? Wait, maybe I misread.

Actually, looking carefully:

In problem 1:

- (i): line with negative slope → eliminate.
- (ii): crosses y-axis at -1 → eliminate.
- (iii): crosses at +1, slope positive 1 → correct.
- (iv): crosses at -1 → eliminate.

So yes, #1 → (iii)

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Problem 2: y = x + 1

Same equation as #1! But different set of graphs.

Check each:

(i): crosses y-axis at -1 → no.

(ii): crosses at 0? Looks like (0,0) → that would be y = x → no.

(iii): crosses at (0,1), and goes up 1 for every 1 right → yes! This is y = x + 1.

(iv): negative slope → no.

✔ So, #2 → (iii)

Wait — but in problem 2, graph (iii) shows a line crossing at (0,1) and going through (1,2), etc. Yes.

But let me check if any other could fit.

Graph (ii) in problem 2: seems to pass through (0,0) and (1,1) → y = x → not x+1.

Graph (i): crosses at -1 → y = x - 1.

So yes, only (iii) fits.

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Problem 3: y = 2x

Slope = 2 → for every 1 unit right, go up 2 units.
Y-intercept = 0 → passes through origin (0,0)

Check graphs:

(i): steep upward slope, passes through (0,0)? Let’s see — yes, appears to go through (0,0) and (1,2) → perfect.

(ii): downward slope → no.

(iii): less steep — looks like slope 1 → y = x → no.

(iv): downward → no.

✔ So, #3 → (i)

Double-check: y=2x at x=1 → y=2; x=-1 → y=-2. Graph (i) shows that.

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Problem 4: y = 2x + 1

Slope = 2 → rise 2, run 1
Y-intercept = 1 → crosses y-axis at (0,1)

Check graphs:

(i): downward slope → no.

(ii): very steep downward → no.

(iii): slope looks like 1, crosses at 1 → that’s y = x + 1 → not enough steepness.

(iv): crosses at (0,1)? Let’s see — yes, and then goes to (1,3) → because 2*1 +1 = 3 → yes! And (-1, -1) → 2*(-1)+1 = -1 → matches.

✔ So, #4 → (iv)

Confirm: at x=0, y=1 → point (0,1). At x=1, y=3 → point (1,3). Graph (iv) shows that.

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Final Answers:

1) (iii)
2) (iii)
3) (i)
4) (iv)

Wait — hold on! In problem 2, the equation is again y = x + 1, but the graphs are different from problem 1. Let me make sure I didn’t mix them up.

Looking back at the original image description (even though I’m not supposed to describe it, I need to verify):

Problem 2 has four graphs labeled (i), (ii), (iii), (iv) below them.

In problem 2:

- Graph (i): line crosses y-axis at -1 → y = x - 1
- Graph (ii): crosses at 0 → y = x
- Graph (iii): crosses at 1, slope 1 → y = x + 1 → correct
- Graph (iv): negative slope → no

Yes, so (iii) is correct for #2.

But now I notice something — in problem 1, the correct graph was also labeled (iii), and in problem 2, also (iii). That’s possible — different sets of graphs.

Similarly, for problem 3, we chose (i), and problem 4, (iv).

All seem consistent.

Let me write final answers clearly.

Final Answer:
1) (iii)
2) (iii)
3) (i)
4) (iv)