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Standard Form & Intercepts — Easy Worksheet 2
Grade 9 · MathSheets Name: ____________________ Date: __________
Write intercepts as ordered pairs, like (4, 0). Write standard form as Ax + By = C with A positive and no common factor.
How to solve
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Example
Find the x-intercept of -2x - 3y = 6.
Answer: (-3, 0)
Not quite. The answer is
💡 The x-intercept is where y = 0. Put y = 0 into −3x + 2y = −18: −3x = −18, so x = −18 ÷ (−3) = 6. The x-intercept is (6, 0).
✓ Correct!
Not quite. The answer is
💡 The x-intercept is where y = 0. Put y = 0 into −3x + 2y = −18: −3x = −18, so x = −18 ÷ (−3) = 6. The x-intercept is (6, 0).
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of 3x + 3y = 3.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The y-intercept is where x = 0. Put x = 0 into x + 2y = 6: 2y = 6, so y = 6 ÷ 2 = 3. The y-intercept is (0, 3).
✓ Correct!
Not quite. The answer is
💡 The y-intercept is where x = 0. Put x = 0 into x + 2y = 6: 2y = 6, so y = 6 ÷ 2 = 3. The y-intercept is (0, 3).
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of -x - 4y = -8.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract 2x from both sides: 2y = −2x + 10. Divide every term by 2: y = −x + 5.
✓ Correct!
Not quite. The answer is
💡 Subtract 2x from both sides: 2y = −2x + 10. Divide every term by 2: y = −x + 5.
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of 3x + 4y = -12.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 From (−6, 0) to (0, 3): rise = 3 − 0 = 3 and run = 0 − (−6) = 6. Slope = rise/run = 36 = 12. The line crosses the y-axis at (0, 3), so b = 3 and y = 1/2x + 3. Multiply every term by 2 to clear the fraction: 2y = x + 6. Subtract x from both sides: −x + 2y = 6. Multiply both sides by −1 so A is positive: x − 2y = −6.
✓ Correct!
Not quite. The answer is
💡 From (−6, 0) to (0, 3): rise = 3 − 0 = 3 and run = 0 − (−6) = 6. Slope = rise/run = 36 = 12. The line crosses the y-axis at (0, 3), so b = 3 and y = 1/2x + 3. Multiply every term by 2 to clear the fraction: 2y = x + 6. Subtract x from both sides: −x + 2y = 6. Multiply both sides by −1 so A is positive: x − 2y = −6.
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of -x - 4y = -12.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The x-intercept is where y = 0. Put y = 0 into x − 2y = 4: x = 4. The x-intercept is (4, 0).
✓ Correct!
Not quite. The answer is
💡 The x-intercept is where y = 0. Put y = 0 into x − 2y = 4: x = 4. The x-intercept is (4, 0).
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of x + 3y = 9.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The y-intercept is where x = 0. Put x = 0 into 4x + 3y = 24: 3y = 24, so y = 24 ÷ 3 = 8. The y-intercept is (0, 8).
✓ Correct!
Not quite. The answer is
💡 The y-intercept is where x = 0. Put x = 0 into 4x + 3y = 24: 3y = 24, so y = 24 ÷ 3 = 8. The y-intercept is (0, 8).
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of 3x - 4y = -12.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Add 4x to both sides: −y = 4x + 2. Divide every term by (−1): y = −4x − 2.
✓ Correct!
Not quite. The answer is
💡 Add 4x to both sides: −y = 4x + 2. Divide every term by (−1): y = −4x − 2.
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of x - y = 2.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 From (−3, 0) to (0, 1): rise = 1 − 0 = 1 and run = 0 − (−3) = 3. Slope = rise/run = 13. The line crosses the y-axis at (0, 1), so b = 1 and y = 1/3x + 1. Multiply every term by 3 to clear the fraction: 3y = x + 3. Subtract x from both sides: −x + 3y = 3. Multiply both sides by −1 so A is positive: x − 3y = −3.
✓ Correct!
Not quite. The answer is
💡 From (−3, 0) to (0, 1): rise = 1 − 0 = 1 and run = 0 − (−3) = 3. Slope = rise/run = 13. The line crosses the y-axis at (0, 1), so b = 1 and y = 1/3x + 1. Multiply every term by 3 to clear the fraction: 3y = x + 3. Subtract x from both sides: −x + 3y = 3. Multiply both sides by −1 so A is positive: x − 3y = −3.
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
Try a similar one
Find the x-intercept of x + y = 1.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Standard Form & Intercepts — Easy Worksheet 2
Write intercepts as ordered pairs, like (4, 0). Write standard form as Ax + By = C with A positive and no common factor.