# How do you find the x and y intercepts of 5y=7.5-2.5x?

Sep 9, 2016

${y}_{\text{intercept}} = \frac{3}{2}$

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

#### Explanation:

Lets get rid of the decimals. Multiply both sides by 2

$2 \left(5 y\right) = 2 \left(7.5 - 2.5 x\right)$

$10 y = 15 - 5 x$

Divide both sides by 10

$y = \frac{15}{10} - \frac{5}{10} x$

$y = \frac{3}{2} - \frac{1}{2} x$
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y intercept is at $x = 0$ so by substitution

y_("intercept")" "=" "3/2-1/2(0)" "=" "3/2

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x intercept is at $y = 0$ so by substitution

$0 = \frac{3}{2} - \frac{1}{2} \left({x}_{\text{intercept}}\right)$

$\implies + \frac{1}{2} \left({x}_{\text{intercept}}\right) = \frac{3}{2}$

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

Sep 9, 2016

x intercept is 3
y intercept is 1.5

#### Explanation:

To find x intercept we should substitute $y$ by zero
To find y intercept we should substitute $x$ by zero

x intercept for the given equation:
$5 \left(0\right) = 7.5 - 2.5 x$
$\Rightarrow 0 = 7.5 - 2.5 x$
$\Rightarrow 0 = 7.5 - 2.5 x$
$\Rightarrow - 7.5 = - 2.5 x$
$\Rightarrow x = \frac{- 7.5}{-} 2.5$
$\Rightarrow x = 3$

y intercept of the given equation:
$5 y = 7.5 - 2.5 \left(0\right)$
$\Rightarrow 5 y = 7.5 - 0$
$\Rightarrow 5 y = 7.5$
$\Rightarrow y = \frac{7.5}{5}$
$\Rightarrow y = 1.5$

Therefore, x intercept is 3 and y intercept is 1.5