Question

Writing to Learn x- and y-intercepts

Answer 1

The x and y intercepts of a line are when $y=0$ and $x=0$ respectively.

• c and d are the x and y intercepts because they represent C/A and B/A in the standard linear equation

• The x and the y intercepts are related to c and d because they represent the values of the equation when y and x equals 0 respectively.

The given equation is:

$\frac xc + \frac yd = 1$

(1) Why c and d are the intercepts

We have:

$\frac xc + \frac yd = 1$

Multiply through by cd

$cd \times \frac xc + cd \times \frac yd = cd \times1$

$dx + cy = cd$

A linear equation is represented as:

$Ax + By = C$

Where:

$\frac CA \to$ x intercept

$\frac BA \to$ y intercept

So, by comparing $Ax + By = C$ to $dx + cy = cd$

$\frac CA \to d \to$ The x-intercept

$\frac CB \to c \to$ The y-intercept

(b) How the intercepts are related to c and d?

In (a) above, we have:

$\frac CA \to d \to$ The x-intercept

$\frac CB \to c \to$ The y-intercept

When $x = 0$

We have:

$dx + cy = cd$

$d \times 0 + cy = cd$

$cy = cd$

Divide by c

$y = d$ ---- the y-intercept

When $y = 0$

We have:

$dx + cy = cd$

$dx + c \times 0 = cd$

$dx = cd$

Divide by d

$x =d$ ---- the x-intercept

Read more about intercepts at:

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