As shown in the graph, the line is a straight line. Therefore, the general equation of a straight line can be employed to derive the equation of the line.

The general equation of a straight line is given by:

y = mx + c <em>or </em>-------------(i)

y - y₁ = m(x - x₁) -----------------(ii)

Where;

y₁ is the value of a point on the y-axis

x₁ is the value of the same point on the x-axis

m is the slope of the line

c is the y-intercept of the line.

Equation (i) is the slope-intercept form of a line

Steps:

(i) Pick any two points (x₁, y₁) and (x₂, y₂) on the line.

In this case, let;

(x₁, y₁) = (0, 3)

(x₂, y₂) = (4, -2)

(ii) With the chosen points, calculate the slope <em>m</em> given by;

m = $\frac{y_2 - y_1}{x_2-x_1}$

m = $\frac{-2-3}{4-0}$

m = $\frac{-5}{4}$

(iii) Substitute the first point (x₁, y₁) = (0, 3) and m = $\frac{-5}{4}$ into equation (ii) as follows;

y - 3 = $\frac{-5}{4}$ (x - 0)

(iv) Solve for y from (iii)

y - 3 = $\frac{-5}{4}$ x

y = $\frac{-5}{4}$ x + 3 [This is the slope intercept form of the line]

Where the slope is $\frac{-5}{4}$ and the intercept is 3

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3 years ago