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Determine the equation of the line whose gradient is 2 and passes through the point (0, 4).

Mathematics

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Answer

y=2x+4y = 2x + 4

Step-by-step solution

3 steps

Let's solve question 1(a) first.

Question 1(a): Determine the equation of the line whose gradient is 2 and passes through the point $(0, 4)$.

  1. Identify the given information.

    The gradient (slope) is m=2m = 2.
    The line passes through the point (x1,y1)=(0,4)(x_1, y_1) = (0, 4).

  2. Use the point-slope form of a linear equation.

    The point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).
    Substitute the given values:

    y−4=2(x−0)y - 4 = 2(x - 0)

  3. Simplify the equation.

    y−4=2xy - 4 = 2x

    Add 4 to both sides to express the equation in the slope-intercept form (y=mx+cy = mx + c):

    y=2x+4y = 2x + 4
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