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

Hint: 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 \[y = - 4\].