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Writing Equations of Lines (Point-Slope Form) — Easy Worksheet 2
Grade 9 · MathSheets Name: ____________________ Date: __________
Write an equation of each line in the form asked for. Write fractional slopes like y = 2/3x + 1.
How to solve
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Example
Write an equation in slope-intercept form of the line with slope -2 that passes through (0, 4).
Answer: y = -2x + 4
Not quite. The answer is
💡 Put m = 4 and (4, 10) into y = mx + b: 10 = 4(4) + b, so 10 = 16 + b. Subtract 16 from both sides: b = 10 − 16 = −6. So the equation is y = 4x − 6.
✓ Correct!
Not quite. The answer is
💡 Put m = 4 and (4, 10) into y = mx + b: 10 = 4(4) + b, so 10 = 16 + b. Subtract 16 from both sides: b = 10 − 16 = −6. So the equation is y = 4x − 6.
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope 1 that passes through (-2, 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
💡 Point-slope form is y − y1 = m(x − x1). Put in m = −5 and (9, 2): y − 2 = −5(x − 9).
✓ Correct!
Not quite. The answer is
💡 Point-slope form is y − y1 = m(x − x1). Put in m = −5 and (9, 2): y − 2 = −5(x − 9).
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope 2 that passes through (2, 1).
✓ 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 (0, 3) to (2, 5): rise = 5 − 3 = 2 and run = 2 − 0 = 2. Slope = rise/run = 22 = 1. Put m = 1 and (0, 3) into y = mx + b: 3 = 1(0) + b, so b = 3. So the equation is y = x + 3.
✓ Correct!
Not quite. The answer is
💡 From (0, 3) to (2, 5): rise = 5 − 3 = 2 and run = 2 − 0 = 2. Slope = rise/run = 22 = 1. Put m = 1 and (0, 3) into y = mx + b: 3 = 1(0) + b, so b = 3. So the equation is y = x + 3.
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope -2 that passes through (-2, -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
💡 The line crosses the y-axis at (0, 0), so b = 0. From (0, 0) to (1, 1): rise = 1 − 0 = 1 and run = 1 − 0 = 1. Slope = rise/run = 11 = 1. So the equation is y = x.
✓ Correct!
Not quite. The answer is
💡 The line crosses the y-axis at (0, 0), so b = 0. From (0, 0) to (1, 1): rise = 1 − 0 = 1 and run = 1 − 0 = 1. Slope = rise/run = 11 = 1. So the equation is y = x.
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope 4 that passes through (3, 15).
✓ 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
💡 Put m = −3 and (−4, 5) into y = mx + b: 5 = −3(−4) + b, so 5 = 12 + b. Subtract 12 from both sides: b = 5 − 12 = −7. So the equation is y = −3x − 7.
✓ Correct!
Not quite. The answer is
💡 Put m = −3 and (−4, 5) into y = mx + b: 5 = −3(−4) + b, so 5 = 12 + b. Subtract 12 from both sides: b = 5 − 12 = −7. So the equation is y = −3x − 7.
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope 4 that passes through (0, 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
💡 Point-slope form is y − y1 = m(x − x1). Put in m = 3 and (7, −7): y − (−7) = 3(x − 7), which simplifies to y + 7 = 3(x − 7).
✓ Correct!
Not quite. The answer is
💡 Point-slope form is y − y1 = m(x − x1). Put in m = 3 and (7, −7): y − (−7) = 3(x − 7), which simplifies to y + 7 = 3(x − 7).
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope 1 that passes through (1, -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, −1) to (−1, −3): rise = −3 − (−1) = −2 and run = −1 − (−3) = 2. Slope = rise/run = −22 = −1. Put m = −1 and (−3, −1) into y = mx + b: −1 = −1(−3) + b, so −1 = 3 + b. Subtract 3 from both sides: b = −1 − 3 = −4. So the equation is y = −x − 4.
✓ Correct!
Not quite. The answer is
💡 From (−3, −1) to (−1, −3): rise = −3 − (−1) = −2 and run = −1 − (−3) = 2. Slope = rise/run = −22 = −1. Put m = −1 and (−3, −1) into y = mx + b: −1 = −1(−3) + b, so −1 = 3 + b. Subtract 3 from both sides: b = −1 − 3 = −4. So the equation is y = −x − 4.
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope 2 that passes through (-1, -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
💡 The line crosses the y-axis at (0, −3), so b = −3. From (0, −3) to (1, −1): rise = −1 − (−3) = 2 and run = 1 − 0 = 1. Slope = rise/run = 21 = 2. So the equation is y = 2x − 3.
✓ Correct!
Not quite. The answer is
💡 The line crosses the y-axis at (0, −3), so b = −3. From (0, −3) to (1, −1): rise = −1 − (−3) = 2 and run = 1 − 0 = 1. Slope = rise/run = 21 = 2. So the equation is y = 2x − 3.
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
Try a similar one
Write an equation in slope-intercept form of the line with slope 3 that passes through (0, -9).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Writing Equations of Lines (Point-Slope Form) — Easy Worksheet 2
Write an equation of each line in the form asked for. Write fractional slopes like y = 2/3x + 1.