Question

How do you graph using the intercepts for$6x-y=4$?

Answer 1

Hint : In order to graph plot for the equation,$6x-y=4$, we need the points to be plotted in the graph, however here, we need to draw using the intercepts , for this, we can find the two intercepts , $x-$and $y-$intercepts by putting $x$and $y$zero one by one and then simply plotting the intercepts.

Complete step-by-step answer :
Firstly let us write the equation, for which we need to plot the graph
$6x-y=4$
Let us find the $x-$and $y-$intercepts
Now, to find the$x-$intercept, put $y=0$in the equation
i.e.

$$6x-y=4 \\\ \Rightarrow 6x-0=4 \\\ \Rightarrow 6x=4 \\\ \Rightarrow x=\dfrac{4}{6}=\dfrac{2}{3} \;$$

Therefore, the $x-$intercept is $\dfrac{2}{3}$
Now, let us find the$y-$intercept
For this, let us put $x=0$in the equation

$$6x-y=4 \\\ \Rightarrow 6\left( 0 \right)-y=4 \\\ \Rightarrow -y=4 \\\ \Rightarrow y=-4 \;$$

Thus, we get the $y-$intercept, which is $-4$
Therefore, we get the intercept points as
$\left( \dfrac{2}{3},0 \right)$and$\left( 0,-4 \right)$
Now, if we plot these two points in the graph, we get

Now, this equation is for a straight line graph for which the intercepts have been drawn
If we join the two points, we get the graph as required

Hence, the graph is plotted.

Note : The formula used for the graph is for finding the intercepts. For finding $x-$intercept, first put $y=0$in the equation and in order to find the $y-$intercept, put $x=0$, in this way the two points for the graph are found and then plotted to get a straight line graph.
Alternatively, this can also be solved by looking at the equation,

$$6x-y=4 \\\ y=6x-4 \;$$

This equation is of the form $y=mx+c$
Where, $m$is the slope and $c$is the$y-$ intercept,
And $x-$intercept is found in the same way as before.