Question

How do you find the x and y intercept of $4x+y=4$?

Answer 1

Change of form of the given equation will give the x intercept and y intercept of the line $4x+y=4$. We get into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$ to find the x intercept, and y intercept of the line as p and q respectively. we also change it to the form of $y=mx+k$ to find the slope m.

Complete step-by-step solution:
The given equation $4x+y=4$ is in the form of $ax+by=c$. Here a, b, c are the constants.
Now we have to find the x intercept, and y intercept of the same line $4x+y=4$.
For this we convert the given equation into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$. From the intercept form we get that the x intercept, and y intercept of the line will be p and q respectively.
The given equation is $4x+y=4$. Converting into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$, we get
$\begin{aligned} & 4x+y=4 \\\ & \Rightarrow \dfrac{4x}{4}+\dfrac{y}{4}=1 \\\ & \Rightarrow \dfrac{x}{1}+\dfrac{y}{4}=1 \\\ \end{aligned}$
Therefore, the x intercept, and y intercept of the line $4x+y=4$ is 1 and 4 respectively.
The intercepting points for the line with the axes are $\left( 1,0 \right)$ and $\left( 0,4 \right)$ respectively.

The changed form of $y=-4x+4$ from $4x+y=4$ is in the slope form of $y=mx+k$. This gives the slope of the line $4x+y=4$ as $-4$.

Note: A line parallel to the X-axis does not intersect the X-axis at any finite distance and hence we cannot get any finite x-intercept of such a line. Same goes for lines parallel to the Y-axis. In case of slope of a line the range of the slope is 0 to $\infty$.