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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

General form, and changing between the forms of a line

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 16 s
  • British Columbia
  • BC10-MA-16

The video introduces general form Ax + By + C = 0 (A, B and C integers, A not negative) beside slope-intercept form y = mx + b. It turns y = −2x + 11 into 2x + y − 11 = 0, then turns 3x − 4y + 8 = 0 back into y = 3/4 x + 2 by dividing every term by −4, reading off slope 3/4 and y-intercept 2. It checks each answer with a point, shows the mistake of dividing only some terms (y = 3/4 x − 8), and ends with a one-line recap.

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In one sentence

The question this lesson answers

Slope-intercept form is y equals m x plus b.

m is the slope, or steepness, and b is the y-intercept, where the line crosses the y-axis.

Transcript

What the lesson says

Slope-intercept form is y equals m x plus b.

m is the slope, or steepness, and b is the y-intercept, where the line crosses the y-axis.

General form is A x plus B y plus C equals zero, with every term on one side.

A, B and C are integers, so no fractions, and A is not negative.

Write y equals negative 2 x plus 11 in general form.

Add 2 x to both sides, so the x term is positive: 2 x plus y equals 11.

Subtract 11 from both sides: 2 x plus y minus 11 equals zero.

So A is 2, B is 1, because y means 1 y, and C is negative 11.

Check with x equals 1, where y is 9: 2 times 1, plus 9, minus 11, is 0.

Now go back: find the slope and y-intercept of 3 x minus 4 y plus 8 equals zero.

Subtract 3 x and 8 from both sides: negative 4 y equals negative 3 x minus 8.

Now divide every term by negative 4, on both sides.

Negative 4 y over negative 4 is y. Negative 3 x over negative 4 is 3 over 4 x. Minus 8 over negative 4 is plus 2.

Now read them off: the slope is 3 over 4, and the y-intercept is 2.

Check with x equals 4, where y is 5: 3 times 4, minus 4 times 5, plus 8, is 0.

A common mistake is dividing only some terms by negative 4. Forget the 8, and you get y equals 3 over 4 x minus 8, which is wrong.

To recap: for general form, move every term to one side. To go back, get y alone and divide every term.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Linear relations: linear functions: slope and equations of linesBC10-MA-16

Previous: Point-slope form: a line from one point and its slopeNext: Parallel and perpendicular lines: equal slopes and negative reciprocals

The outcomes and strands follow the British Columbia curriculum.

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