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Calculate the gradient of the two lines below.

Mathematics

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Answers

2 parts
a

−35-\frac{3}{5}

b

32\frac{3}{2}

Step-by-step solution

7 steps

To work out the gradient of the lines, we use the formula:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Part a· 3 steps

For the first line

  1. Identify two clear points on the line.

    We can see the line passes through (−3,0)(-3, 0) and (2,−3)(2, -3).
    Let (x1,y1)=(−3,0)(x_1, y_1) = (-3, 0) and (x2,y2)=(2,−3)(x_2, y_2) = (2, -3).

  2. Substitute the coordinates into the gradient formula.

    ma=−3−02−(−3)m_a = \frac{-3 - 0}{2 - (-3)}

  3. Calculate the gradient.

    ma=−32+3=−35m_a = \frac{-3}{2 + 3} = \frac{-3}{5}

    The gradient of line (a) is −35\boxed{-\frac{3}{5}}.

Part b

32\frac{3}{2}

For the second line

  1. Identify two clear points on the line.

    We can see the line passes through (0,−3)(0, -3) and (6,6)(6, 6).
    Let (x1,y1)=(0,−3)(x_1, y_1) = (0, -3) and (x2,y2)=(6,6)(x_2, y_2) = (6, 6).

  2. Substitute the coordinates into the gradient formula.

    mb=6−(−3)6−0m_b = \frac{6 - (-3)}{6 - 0}

  3. Calculate the gradient.

    mb=6+36=96m_b = \frac{6 + 3}{6} = \frac{9}{6}

  4. Simplify the fraction.

    mb=32m_b = \frac{3}{2}

    The gradient of line (b) is 32\boxed{ \frac{3}{2}}.

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