What are the intercepts of the line y = 1/2x-3?

Sep 28, 2015

x-intercept $= 6$
y-intercept $= - 3$

Explanation:

The x-intercept is the point where the graph crosses the X-axis; for all point on the X-axis, $y = 0$
Substituting $0$ for $y$ in $y = \frac{1}{2} x - 3$
we get
$\textcolor{w h i t e}{\text{XXX}} 0 = \frac{1}{2} x - 3$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} \frac{1}{2} x = 3$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} x = 6$

Similarly, the y-intercept is the point where the graph crosses the Y-axis; and for all point on the Y-axi, $x = 0$
Substituting $0$ for $x$ in $y = \frac{1}{2} x - 3$
we get
$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{2} \cdot \left(0\right) - 3$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} y = - 3$

Sep 28, 2015

You set $x$ and $y$ to $= 0$ in turn
$y$-intercept is when $x = 0$
Then $y = - 3 \to \left(0 , - 3\right)$
$x$-intercept is when $y = 0$
$\frac{1}{2} x - 3 = 0 \to \frac{1}{2} x = 3 \to x = 6 \to \left(6 , 0\right)$