The x and y intercepts of a line are when [tex]y=0[/tex] and [tex]x=0[/tex] respectively.
The given equation is:
[tex]\frac xc + \frac yd = 1[/tex]
(1) Why c and d are the intercepts
We have:
[tex]\frac xc + \frac yd = 1[/tex]
Multiply through by cd
[tex]cd \times \frac xc + cd \times \frac yd = cd \times1[/tex]
[tex]dx + cy = cd[/tex]
A linear equation is represented as:
[tex]Ax + By = C[/tex]
Where:
[tex]\frac CA \to[/tex] x intercept
[tex]\frac BA \to[/tex] y intercept
So, by comparing [tex]Ax + By = C[/tex] to [tex]dx + cy = cd[/tex]
[tex]\frac CA \to d \to[/tex] The x-intercept
[tex]\frac CB \to c \to[/tex] The y-intercept
(b) How the intercepts are related to c and d?
In (a) above, we have:
[tex]\frac CA \to d \to[/tex] The x-intercept
[tex]\frac CB \to c \to[/tex] The y-intercept
When [tex]x = 0[/tex]
We have:
[tex]dx + cy = cd[/tex]
[tex]d \times 0 + cy = cd[/tex]
[tex]cy = cd[/tex]
Divide by c
[tex]y = d[/tex] ---- the y-intercept
When [tex]y = 0[/tex]
We have:
[tex]dx + cy = cd[/tex]
[tex]dx + c \times 0 = cd[/tex]
[tex]dx = cd[/tex]
Divide by d
[tex]x =d[/tex] ---- the x-intercept
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