Question

How do you find the slope and intercept of \[3x+y=6\]?

Answer 1

Hint: In this problem, we have to find the slope and intercept of the given equation. We can find the slope and y-intercept using slope-intercept form. We know that the general equation of the slope-intercept form is \[y=mx+c\], where m is the slope and c is the y-intercept. We can write the given equation as slope-intercept form and go find the slope value. We know that at x-intercept, the value of y is 0. We can find the slope and intercept.

Complete step by step answer:
We know that the given equation is,
\[3x+y=6\]
We can write the given equation as,
\[y=-3x+6\] …… (1)
We also know that the general equation of slope intercept form is,
 \[y=mx+c\] ……. (2)
Where, m = slope, c = y-intercept.
Now we can compare the equation (1) and the equation (2), we get
Slope, m = -3
y-intercept, c = 6.
We know that at y-intercept x is 0.
Therefore, y-intercept is \[\left( 0,6 \right)\]
We know that at x-intercept, y is 0.
We can substitute the value of y in (1), we get
\[\begin{align}
  & \Rightarrow 0=-3x+6 \\
 & \Rightarrow 3x=6 \\
 & \Rightarrow x=2 \\
\end{align}\]
Therefore, x-intercept is \[\left( 2,0 \right)\]
Therefore, the y-intercept is \[\left( 0,6 \right)\], x-intercept is \[\left( 2,0 \right)\] and the value of slope is -3.
Now we can plot the graph using the y-intercept \[\left( 0,6 \right)\], x-intercept \[\left( 2,0 \right)\].

Note:
Students make mistakes in sign part, while changing the given equation to slope intercept form. We should know that at x-intercept, the value of y is 0 and at y-intercept, the value of x is 0, substituting the value of x and y separately in the given equation, we can get the x-intercept and the y-intercept.