Question

1. write the equation in standard form of the line that has x-intercept 3 and y-intercept 5.

Explanation:

Step1: Recall intercept form

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

Step2: Convert to standard form

The standard form of a line is $Ax + By = C$, where $A$, $B$, and $C$ are integers and $A\geq0$. To eliminate the denominators in $\frac{x}{3}+\frac{y}{5}=1$, we multiply each term by the least common multiple of 3 and 5, which is 15.
$15\times\frac{x}{3}+15\times\frac{y}{5}=15\times1$
Simplifying, we get $5x + 3y = 15$.

Answer:

$5x + 3y = 15$