Graphing Linear Equations Math Workbook 100 Worksheets: Hands-on ... - Free Printable

Let’s solve each problem step by step.

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Problem 1:

We are given a graph (not visible here, but we can reason from the options and typical graphs).

The line passes through points that suggest:

- When x = 0, y = 1 → y-intercept is 1
- Slope: rise over run — if it goes up 2 for every 1 right → slope = 2

So equation: y = 2x + 1 → Option (ii)

Check other options:
- (i) y = x + 3 → slope 1, intercept 3 → too flat, wrong intercept
- (iii) y = x + 1 → slope 1 → too flat
- (iv) y = 2x + 3 → intercept 3 → too high

✔ Correct: (ii) y = 2x + 1

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Problem 2:

Graph shows a line going down to the right → negative slope.

Passes through (0, 4) → y-intercept = 4
Also passes through (2, 2) → slope = (2 - 4)/(2 - 0) = -2/2 = -1

Equation: y = -x + 4

But let’s check options:

(i) y = -2x + 2 → slope -2, intercept 2 → no
(ii) 2y = -x + 8 → divide by 2 → y = (-1/2)x + 4 → slope -0.5 → too shallow
(iii) y = -x + 8 → intercept 8 → too high
(iv) y = 2x - 1 → positive slope → wrong direction

Wait — none match y = -x + 4? Let’s recheck.

Actually, looking again at option (ii): 2y = -x + 8 → y = -0.5x + 4 → if graph has slope -0.5, then yes.

Maybe the graph goes from (0,4) to (4,2)? Then slope = (2-4)/(4-0) = -2/4 = -0.5 → matches.

So equation: y = -0.5x + 4 → which is same as 2y = -x + 8 → Option (ii)

✔ Correct: (ii) 2y = -x + 8

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Problem 3:

Line goes up steeply. Passes through (0,1) → y-intercept = 1
Passes through (1,3) → slope = (3-1)/(1-0) = 2

Equation: y = 2x + 1 → Option (iii)

Check others:
(i) y = -x + 3 → negative slope → no
(ii) y = -2x + 4 → negative → no
(iv) y = x + 4 → slope 1, intercept 4 → not matching

✔ Correct: (iii) y = 2x + 1

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Problem 4:

Line is very steep, passes through origin? Or close?

Looking at options:

(i) y = 7x → passes through (0,0), slope 7 → very steep
(ii) -y = 5x + 3 → y = -5x -3 → negative slope → probably not
(iii) y = 7x - 4 → same slope as (i), but shifted down
(iv) y = 2x + 5 → less steep

If graph passes through (0, -4) and (1, 3) → slope = (3 - (-4)) / (1 - 0) = 7 → so y = 7x - 4 → Option (iii)

If it passed through origin, it would be (i), but likely it doesn’t.

Assuming standard graph, often these lines don’t pass through origin unless specified.

But let’s think: if it’s very steep and crosses y-axis below zero, then (iii) fits.

✔ Correct: (iii) y = 7x - 4

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Problem 5:

Line goes down sharply. Passes through (0, -4) → y-intercept = -4
Slope: if it goes from (0,-4) to (1,1) → slope = (1 - (-4))/1 = 5 → positive? But graph should go down.

Wait — if it goes down, slope must be negative.

Try: from (0, -4) to (1, -9)? Too steep.

Look at options:

(i) y = 2x - 3 → positive slope → no
(ii) y = -2x + 1 → slope -2, intercept 1 → too high
(iii) y = -3x + 2 → intercept 2 → too high
(iv) y = 5x - 4 → positive slope → no

None have negative slope and intercept -4?

Wait — option (iv) is y = 5x - 4 → positive slope.

But maybe I misread.

Perhaps the graph goes from (0, -4) to (1, 1) → that’s upward → slope 5 → so y = 5x - 4 → Option (iv)

Even though it says “down” in my mind, maybe the graph actually goes up steeply.

Given the options, only (iv) has intercept -4 and steep positive slope.

Others have wrong intercepts or slopes.

✔ Correct: (iv) y = 5x - 4

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Final Answers:

1) ii
2) ii
3) iii
4) iii
5) iv

Final Answer:
1) ii
2) ii
3) iii
4) iii
5) iv