Question

How do you find the $x$ and $y$ intercepts of $x+5y=-15$?

Answer 1

Before solving the above question, let me tell you what intercept means in mathematics. The intercepts of a graph are the points at which the graph crosses the axis. In the same way the x-intercepts means it is a point at which the graph crosses the x-axis and at this point the y-coordinate is always zero. The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero. It simply means if we have to determine the x-intercept we have to set $y$ equals to zero and solve for $x$. Similarly, if we have to determine the y-intercept then we have to set $x$ equals to zero and solve for $y$.

Complete step by step solution:
The given equation which we have to find the intercepts of $x$ and $y$ is:
$\Rightarrow x+5y=-15$
Now by using this equation we have to find intercepts of $x$ and $y$.
Now to find the x-intercept of the given equation $x+5y=-15$, then set $y=0$ in the given equation then we get,
$\begin{aligned} & \Rightarrow x+5\left( 0 \right)=-15 \\\ & \Rightarrow x=-15 \\\ \end{aligned}$
The x-intercept of the given equation $x+5y=-15$ is $-15$
Similarly to find the intercept of $y$ from the given equation$x+5y=-15$, we have to set $x=0$ in the given equation then we get,
$\begin{aligned} & \Rightarrow 0+5y=-15 \\\ & \Rightarrow 5y=-15 \\\ \end{aligned}$
Now dividing the both sides of the equation by$5$, then we get$\Rightarrow y=-3$
The y-intercept of the given equation $x+5y=-15$is$-3$.
Hence we get the intercepts x and y of $x+5y=-15$are$x=-15,y=-3$.

Note: The intercepts are used to draw a graph of any equation. Actually the intercepts are those points where the graph cuts the x and y-axis. By using them we can find where the $x$ and $y$ in the graph so that we can easily draw a line.