# How do you find the x and y intercepts for 4x - y = 10?

Jan 30, 2016

The x-intercept is the point where the y-value is zero, and vice versa. Substituting 0 in for $x$ and $y$ in turn and solving gives $x - \text{intercept"=(10/4,0), y-"intercept} = \left(0 , - 10\right)$.

#### Explanation:

The x-intercept for a function is the point where it crosses the x-axis, and that is the horizontal line '$y = 0$'. Substitute in $y = 0$ in the original equation to find the x-intercept:

$4 x - 0 = 10$
$4 x = 10$
$x = \frac{10}{4}$ $\left(\mathmr{and} 2.5\right)$

The x-intercept, therefore, is the point $\left(\frac{10}{4} , 0\right)$.

Similarly, the y-intercept is the point where the function crosses the y-axis, the line $x = 0$, so substitute in $x = 0$:

$0 - y = 10$
$y = - 10$

So the y-intercept is the point $\left(0 , - 10\right)$.