# How do you find the x and y intercept of 3x − y = 5 ?

Jul 7, 2016

${x}_{\text{intercept}} = \frac{5}{3}$

${y}_{\text{intercept}} = - 5$

#### Explanation:

color(blue)("Determine "y_("intercept"))

The y-axis crosses the x-axis at $x = 0$ so to find the y-intercept substitute $x = 0$ into the equation

color(brown)(3x-y=5)color(blue)(" "->" "3(0)-y=5

But $3 \times 0 = 0$ giving

$- y = 5$

Multiply both sides by $\left(- 1\right)$

$\left(- y\right) \times \left(- 1\right) = 5 \times \left(- 1\right)$

$y = - 5$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(blue)("Determine "x_("intercept"))

The x-axis crosses the y-axis at $y = 0$ so to find the x-intercept substitute $y = 0$ into the equation

color(brown)(3x-y=5)color(blue)(" "->" "3x-0=5

$\textcolor{b r o w n}{3 x = 5}$

Divide both sides by $\textcolor{b l u e}{3}$

color(brown)(3/(color(blue)(3)) xx x=5/(color(blue)(3))

But $\frac{3}{3} = 1$

$x = \frac{5}{3}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{3 x - y = 5} \text{ "->" } \textcolor{b l u e}{y = 3 x - 5}$