Question

regularity write a linear equation in standard form that satisfies the given set of conditions. x-intercept: 3, y-intercept: 5

Explanation:

Step1: Recall intercept form

The intercept form of a linear equation is $\frac{x}{a}+\frac{y}{b} = 1$, where $a$ is the x - intercept and $b$ is the y - intercept. Given $a = 3$ and $b=5$.
So the equation in intercept form is $\frac{x}{3}+\frac{y}{5}=1$.

Step2: Convert to standard form

To convert $\frac{x}{3}+\frac{y}{5}=1$ to standard form $Ax + By=C$ (where $A$, $B$, $C$ are integers and $A\geq0$), we first find a common denominator for the left - hand side, which is 15.
Multiply each term by 15: $15\times\frac{x}{3}+15\times\frac{y}{5}=15\times1$.
Simplify each term: $5x + 3y=15$.

Answer:

The linear equation in standard form is $5x + 3y = 15$.