Algebra 1 Worksheets | Linear Equations Worksheets - Free Printable

Let’s solve each problem one by one. For each, we’re given:

- An ordered pair (x, y) that lies on the line.
- The y-intercept (where the line crosses the y-axis — this is “b” in y = mx + b).
- We need to find the slope (m), then write the full equation.

We’ll use the formula for a line:
y = mx + b

We know b (the y-intercept).
We also know one point (x, y) that satisfies the equation.
So we can plug those into the equation and solve for m.

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Problem 1:

Ordered pair: (-1, 3)
y-intercept: -3 → so b = -3

Plug into y = mx + b:
3 = m(-1) + (-3)
3 = -m - 3
Add 3 to both sides:
6 = -m
Multiply both sides by -1:
m = -6

Equation: y = -6x - 3

✔ Check: Plug x = -1 → y = -6*(-1) - 3 = 6 - 3 = 3 ✔️

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Problem 2:

Ordered pair: (3, -4)
y-intercept: -2 → b = -2

Plug into y = mx + b:
-4 = m(3) + (-2)
-4 = 3m - 2
Add 2 to both sides:
-2 = 3m
Divide by 3:
m = -2/3

Equation: y = (-2/3)x - 2

✔ Check: Plug x = 3 → y = (-2/3)(3) - 2 = -2 - 2 = -4 ✔️

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Problem 3:

Ordered pair: (-4, -1)
y-intercept: 3 → b = 3

Plug into y = mx + b:
-1 = m(-4) + 3
-1 = -4m + 3
Subtract 3 from both sides:
-4 = -4m
Divide by -4:
m = 1

Equation: y = 1x + 3 → or just y = x + 3

✔ Check: Plug x = -4 → y = -4 + 3 = -1 ✔️

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Problem 4:

Ordered pair: (-4, -3)
y-intercept: 3 → b = 3

Plug into y = mx + b:
-3 = m(-4) + 3
-3 = -4m + 3
Subtract 3:
-6 = -4m
Divide by -4:
m = (-6)/(-4) = 3/2

Equation: y = (3/2)x + 3

✔ Check: Plug x = -4 → y = (3/2)*(-4) + 3 = -6 + 3 = -3 ✔️

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Problem 5:

Ordered pair: (3, 0)
y-intercept: 3 → b = 3

Plug into y = mx + b:
0 = m(3) + 3
0 = 3m + 3
Subtract 3:
-3 = 3m
Divide by 3:
m = -1

Equation: y = -x + 3

✔ Check: Plug x = 3 → y = -3 + 3 = 0 ✔️

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Problem 6:

Ordered pair: (3, -3)
y-intercept: -4 → b = -4

Plug into y = mx + b:
-3 = m(3) + (-4)
-3 = 3m - 4
Add 4:
1 = 3m
Divide by 3:
m = 1/3

Equation: y = (1/3)x - 4

✔ Check: Plug x = 3 → y = (1/3)(3) - 4 = 1 - 4 = -3 ✔️

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Problem 7:

Ordered pair: (-4, 2)
y-intercept: 4 → b = 4

Plug into y = mx + b:
2 = m(-4) + 4
2 = -4m + 4
Subtract 4:
-2 = -4m
Divide by -4:
m = (-2)/(-4) = 1/2

Equation: y = (1/2)x + 4

✔ Check: Plug x = -4 → y = (1/2)*(-4) + 4 = -2 + 4 = 2 ✔️

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Problem 8:

Ordered pair: (3, -3)
y-intercept: 1 → b = 1

Plug into y = mx + b:
-3 = m(3) + 1
-3 = 3m + 1
Subtract 1:
-4 = 3m
Divide by 3:
m = -4/3

Equation: y = (-4/3)x + 1

✔ Check: Plug x = 3 → y = (-4/3)(3) + 1 = -4 + 1 = -3 ✔️

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Final Answer:

1) slope (m) = -6, equation: y = -6x - 3
2) slope (m) = -2/3, equation: y = (-2/3)x - 2
3) slope (m) = 1, equation: y = x + 3
4) slope (m) = 3/2, equation: y = (3/2)x + 3
5) slope (m) = -1, equation: y = -x + 3
6) slope (m) = 1/3, equation: y = (1/3)x - 4
7) slope (m) = 1/2, equation: y = (1/2)x + 4
8) slope (m) = -4/3, equation: y = (-4/3)x + 1