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Grade 9 Slope & Equations of Lines Practice

Write and Convert Equations of Lines from Points and Graphs

Given a slope and a point, or just two points, you can write the line's equation — and rewrite it in whichever form you need.

Also known as Class 9 maths — the same topics, whether your school calls it grade, class or year.

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Sample questions

A few samples from this topic — try one, then show the answer.

  1. Write Slope-Intercept Equations Through Two Points

    Find the slope-intercept form equation of the line passing through (3,  13)(3,\; 13) and (8,  18)(8,\; 18)
    Show answer
    Answer:
    y = x + 10

  2. Write a Slope-Intercept Equation from a Slope and One Point

    Select the equation of the line with slope 4 4\, that contains (1, 10)(1,\, 10).
    • y=4x+10y = 4x + 10
    • y=4x+6y = 4x + 6
    • y=4x−6y = 4x - 6
    • y=x+4y = x + 4
    Show answer
    Answer:
    y=4x+6y = 4x + 6

  3. Write Point-Slope Equations from a Slope and One Point

    Convert y  +  y \; + \;8  =  (x  −  \; = \; (x \; - \;2) to y  =  mx  +  b y \; = \; mx \; + \; b\,.
    • y  =  x   −  2y \; = \; x\, \; - \; \text{2}
    • y  =  x   +  10y \; = \; x\, \; + \; \text{10}
    • y  =  x   +  6y \; = \; x\, \; + \; \text{6}
    • y  =  x   −  10y \; = \; x\, \; - \; \text{10}
    Show answer
    Answer:
    y  =  x   −  10y \; = \; x\, \; - \; \text{10}

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A worked example

Find the slope-intercept form equation of the line passing through (3,  13)(3,\; 13) and (8,  18)(8,\; 18)
  1. The slope formula is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Substitute the points (3,  13)(3,\; 13) and (8,  18)(8,\; 18):m=18−138−3=55=1\\[6pt] m = \frac{18 - 13}{8 - 3} = \frac{5}{5} = 1
  2. Now substitute m = 1 and the point (3,  13)(3,\; 13) into y = mx + b:13=1(3)+b13=3+b\\ 13 = 1(3) + b \\ 13 = 3 + b
  3. Solve for b:b=13−3=10\\ b = 13 - 3 = 10
  4. The equation in slope-intercept form is:y=x+10\\ y = x + 10

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