➕ Algebra 1 · Linear Functions

Point-Slope Form: true or false

Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.

All statements and answers

• The line y − 2 = 3(x + 4) passes through the point (4, 2).

  ✗ False. x + 4 is x − (−4), so x₁ = −4 and the line passes through (−4, 2). At x = 4 the right side is 3(8) = 24, which would need y = 26.

• In y + 7 = −(x − 1), the slope is −1.

  ✓ True. −(x − 1) means −1 × (x − 1), so m = −1. The point is (1, −7).

• To write a line through two points in point-slope form, you must find the slope first.

  ✓ True. The form needs m. Find it with the slope formula, then use either point.

• A non-vertical line has exactly one point-slope equation.

  ✗ False. Every point on the line can be the known point, so the line has endless point-slope equations. They all simplify to the same slope-intercept equation.

• The equations y − 4 = 2(x − 1) and y − 8 = 2(x − 3) describe the same line.

  ✓ True. Both have slope 2. The point (3, 8) is on the first line: 8 − 4 = 4 and 2(3 − 1) = 4. Both simplify to y = 2x + 2.

• The vertical line x = −10 can be written in point-slope form by using m = 0.

  ✗ False. m = 0 gives a horizontal line. A vertical line has an undefined slope, so it has no point-slope form.

• The horizontal line through (2, −6) has the point-slope equation y + 6 = 0(x − 2).

  ✓ True. The slope is 0 and y − (−6) = y + 6. The right side is 0, so y = −6.

• The equation y − 5 = 2(x + 3) simplifies to y = 2x + 1.

  ✗ False. Distribute: y − 5 = 2x + 6. Add 5 to both sides: y = 2x + 11.

• In y − 9 = 6(x − 4), putting in x = 4 gives y = 9.

  ✓ True. At x = 4 the right side is 6(0) = 0, so y − 9 = 0 and y = 9. That is the known point (4, 9).

• x − (−2) simplifies to x − 2.

  ✗ False. Subtracting a negative number is the same as adding: x − (−2) = x + 2.

• The line through the origin with slope 3 can be written y − 0 = 3(x − 0).

  ✓ True. The origin is the point (0, 0), so x₁ = 0 and y₁ = 0. This simplifies to y = 3x.

• In point-slope form, you replace x and y with the coordinates of the known point.

  ✗ False. x and y stay as letters. You replace x₁, y₁ and m with numbers.