Question

Determine the intercepts of the line. Do not round your answers. 3x+2y=5

Answer 1

`\textsf{$x$-intercept}: \quad \left((5)/(3),0 \right)`

`\textsf{$y$-intercept}: \quad \left(0,(5)/(2) \right)`

Explanation:

Given equation:

`3x+2y=5`

The x-intercept is when y = 0:

`\implies 3x+2(0)=5`

`\implies 3x=5`

`\implies x=(5)/(3)`

Therefore, the x-intercept is:

`\left((5)/(3),0 \right)`

The y-intercept is when x = 0:

`\implies 3(0)+2y=5`

`\implies 2y=5`

`\impiles y=(5)/(2)`

Therefore, the y-intercept is:

`\left(0,(5)/(2) \right)`