Grade 10 — Mathematics 10C › C10U07 Linear Relations & Functions

Grade 10 › C10U07 Linear Relations & Functions › L9
GRADE 10 · ALBERTAOUTCOME RF7

L9 · Writing the Equation of a Line

Learning goal

“I can write the equation of a linear relation given a graph description, a point and the slope, two points, or a point and a parallel/perpendicular line - by hand, explaining my reasoning - and solve problems with the equation.”

Slope formula — m = (y2 - y1) / (x2 - x1), the same-order subtraction of two points' coordinates.
Substitution — replacing a variable by a known value (e.g. putting a point's coordinates into y = mx + b) to solve for the one remaining unknown.
Two strategies for the equation — substitute into slope-point form directly, or substitute into y = mx + b to find b; both are acceptable, and checking with the second point is mandatory.
Worked example

Graph first: a line is described by its intercepts: it crosses the y-axis at (0, -1) and passes through (3, 5). From the description, b = -1 immediately. Slope = (5 - (-1)) / (3 - 0) = 6 / 3 = 2. Equation: y = 2x - 1. Two points: through (2, 3) and (5, 12): slope = (12 - 3) / (5 - 2) = 9 / 3 = 3. Now substitute one point into y = mx + b: 3 = 3(2) + b -> b = -3. Equation: y = 3x - 3. MANDATORY check with the other point: 3(5) - 3 = 12 - the check is what catches inverted slopes. (The same answer comes from slope-point: y - 3 = 3(x - 2) expands to y = 3x - 3.)

Check yourself — explain it

After finding an equation from two points, checking with the SECOND point matters because...

Paired problem — example still visible

Write the equation of the line through (1, 4) and (3, 10). -> Slope = 6 / 2 = 3; 4 = 3(1) + b -> b = 1; y = 3x + 1. Check: 3(3) + 1 = 10

Faded completion — last step is yours

"Through (0, 2) and (4, 6): slope = ___; b = ___; equation y = ___." -> slope 1; b = 2; y = x + 2

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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