Question

1 find the rule of the following linear function in symmetric form.

2 find the rule of the following linear function in symmetric form.

3 find the rule of the following linear function in symmetric form.
3x - 5y - 15 = 0

4 find the rule of the following linear function in symmetric form.
y = \frac{1}{2}x + 5

5 find the rule of the following linear function in slope - intercept form.\frac{x}{6} + \frac{y}{2} = 1

Explanation:

Problem 1

Step1: Identify intercepts

The x - intercept is \((6,0)\) (so \(a = 6\)) and the y - intercept is \((0,2)\) (so \(b=2\)).

Step2: Symmetric form formula

The symmetric form of a line is \(\frac{x}{a}+\frac{y}{b}=1\). Substitute \(a = 6\) and \(b = 2\).
\(\frac{x}{6}+\frac{y}{2}=1\)

Step1: Identify intercepts

The x - intercept is \((- 4,0)\) (so \(a=-4\)) and the y - intercept is \((0,6)\) (so \(b = 6\)).

Step2: Symmetric form formula

Using \(\frac{x}{a}+\frac{y}{b}=1\), substitute \(a=-4\) and \(b = 6\).
\(\frac{x}{-4}+\frac{y}{6}=1\) or \(-\frac{x}{4}+\frac{y}{6}=1\)

Step1: Find x and y intercepts

For x - intercept, set \(y = 0\): \(3x-15=0\Rightarrow x = 5\) (so \(a = 5\)).
For y - intercept, set \(x = 0\): \(-5y-15=0\Rightarrow y=- 3\) (so \(b=-3\)).

Step2: Symmetric form formula

Using \(\frac{x}{a}+\frac{y}{b}=1\), substitute \(a = 5\) and \(b=-3\).
\(\frac{x}{5}+\frac{y}{-3}=1\) or \(\frac{x}{5}-\frac{y}{3}=1\)

Answer:

\(\frac{x}{6}+\frac{y}{2}=1\)

Problem 2