Question

Equation: $2x - y = 4$ meets
$x$ axis at $( - 4,0)$
$y$ axis at $(0,2)$
$x$ axis at $(2,0)$
$y$ axis at $(0, - 4)$

Answer 1

Here, we have to find the values of $x$ co-ordinate and $y$ co-ordinate where the given line meets the $x$ axis and $y$ axis. We have to find those co-ordinates by using the intercept concept. The point where a curve or a line crosses the axis of the graph is called an intercept. If a point crosses the $x$-axis, then it is said to be $x$-intercept and if a point crosses the $y$-axis, then it is known as $y$-intercept.

Complete step-by-step answer:
The Equation $2x - y = 4$ is an equation of a straight line. The equation of a straight line is of the form $y = mx + c$ where $m$ is the slope or the gradient and $c$ is the $y$ -intercept.
Now, we will find the $x$ - intercept.
Substituting $y = 0$ in the above equation, we get
$\Rightarrow 2x - 0 = 4$
$\Rightarrow 2x = 4$
Dividing both the sides by 2, we get
$\Rightarrow x = 2$
So, the equation meets the $x$ - axis at $x = 2$
Now, we have to find the $y$ - intercept.
Substituting $x = 0$ and solving for $y$ , we have
$\Rightarrow 2(0) - y = 4$
$\Rightarrow - y = 4$
Rewriting the equation, we get
$\Rightarrow y = - 4$
So, the equation meets the $y$ - axis at $y = - 4$
Therefore, the equation $2x - y = 4$ meets the $x$ - axis at $\left( {2,0} \right)$ and the $y$ - axis at $\left( {0, - 4} \right)$ .

Note: We can find the $y$ - intercept from the equation $2x - y = 4$. Rewriting the equation as $y = 2x - 4$ . Since the equation of a straight line is of the form $y = mx + c$ where $m$ is the slope or the gradient and $c$ is the $y$ -intercept. The slope of a line is defined as the ratio of the amount that $y$ increases as $x$ increases some amount. Slope tells us how steep a line is, or how much $y$ increases as $x$ increases. We will get the $x$-intercept as $y = - 4$.