We are given that a line has an x-intercept of 5 and a y-intercept of 3. We need to find the equation of the line.

1. Problem Description

We are given that a line has an x-intercept of 5 and a y-intercept of

3. We need to find the equation of the line.

2. Solution Steps

The intercept form of a linear equation is given by

$\frac{x}{a} + \frac{y}{b} = 1$

where $a$ is the x-intercept and $b$ is the y-intercept.

In this case, the x-intercept is $a = 5$ and the y-intercept is $b = 3$.

Plugging these values into the intercept form, we get:

$\frac{x}{5} + \frac{y}{3} = 1$

To get rid of the fractions, we can multiply the entire equation by the least common multiple of 5 and 3, which is

1

5. $15(\frac{x}{5} + \frac{y}{3}) = 15(1)$

$15(\frac{x}{5}) + 15(\frac{y}{3}) = 15$

$3x + 5y = 15$

We can rewrite this equation in slope-intercept form, which is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept.

$5y = -3x + 15$

$y = \frac{-3}{5}x + \frac{15}{5}$

$y = -\frac{3}{5}x + 3$

3. Final Answer

The equation of the line is $3x + 5y = 15$ or $y = -\frac{3}{5}x + 3$.