Answer:
[tex]y = -\frac{1}{3}x + \frac{8}{3}[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-1,3)[/tex]
[tex]Intercept\ on\ x-axis = Intercept\ on\ y-axis.[/tex]
Required
Determine the equation
First, we calculate the intercepts using:
[tex]\frac{x}{a} + \frac{y}{b} = 1[/tex]
Where
b = Intercept on y axis.
a = Intercept on x axis.
From the question:
[tex]a = 3b[/tex]
The equation becomes:
[tex]\frac{x}{3b} + \frac{y}{b} = 1[/tex]
Multiply through by 3b
[tex]x + 3y = 3b[/tex]
We have: [tex](x_1,y_1) = (-1,3)[/tex]
So:
[tex]-1 + 3 * 3 = 3b[/tex]
[tex]8 = 3b[/tex]
Make b the subject
[tex]b = \frac{8}{3}[/tex]
Substitute [tex]b = \frac{8}{3}[/tex] in [tex]x + 3y = 3b[/tex] to get the equation
[tex]x + 3y = 3 * \frac{8}{3}[/tex]
[tex]x + 3y = 8[/tex]
Make 3y the subject
[tex]3y = -x + 8[/tex]
Make y the subject
[tex]y = -\frac{1}{3}x + \frac{8}{3}[/tex]
