Question

How do you graph using slope and intercept of $2x+y=8$?

Answer 1

Change of form of the given equation will give the slope, y intercept, and x-intercept of the line $2x+y=8$. We change it to the form of $y=mx+k$ to find the slope m. Then, 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. then we place the line on the graph based on that

Complete step by step answer:
We are taking the general equation of line to understand the slope and the intercept form of the line $2x+y=8$.
The given equation $2x+y=8$ is of the form $ax+by=c$. Here a, b, c are the constants.
We convert the form to $y=mx+k$. m is the slope of the line.
So, converting the equation we get
$\begin{aligned} & 2x+y=8 \\\ & \Rightarrow y=-2x+8 \\\ \end{aligned}$
This gives that the slope of the line $2x+y=8$ is -2.
Now we have to find the y intercept, and x-intercept of the same line $2x+y=8$.
For this we convert the given equation into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$. From the form we get that the x intercept, and y intercept of the line will be p and q respectively.
The given equation is $2x+y=8$. Converting into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$, we get
$\begin{aligned} & 2x+y=8 \\\ & \Rightarrow \dfrac{2x}{8}+\dfrac{y}{8}=1 \\\ & \Rightarrow \dfrac{x}{4}+\dfrac{y}{8}=1 \\\ \end{aligned}$
Therefore, the x intercept, and y intercept of the line $2x+y=5$ is 4 and 8 respectively.

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 $\infty$.