Question

How do you find the slope and intercept to graph $y = - \dfrac{1}{6}x + 6$?

Answer 1

We will first write the general equation of a line which is given by $y = mx + c$ and then find the slope by comparing and then we will put $x$ zero in given equation $y = - \dfrac{1}{6}x + 6$ to find $y$ - intercept and then $y = 0$ to find the $x$ – intercept.

Complete step by step solution:
We are given that we are required to find the slope and the intercept of $y = - \dfrac{1}{6}x + 6$.
The general equation of a line is given by $y = mx + c$, where m is the slope of the line.
Now, we are given the line $y = - \dfrac{1}{6}x + 6$. If we compare this to the above mentioned line, we will then obtain: $m = - \dfrac{1}{6}$ and c = 6.
Therefore, the slope of the given line is $- \dfrac{1}{6}$.
Now, we need to find the intercepts of the line $y = - \dfrac{1}{6}x + 6$.
Let us put in $x = 0$ in the equation $y = - \dfrac{1}{6}x + 6$ to find the $y$ – intercept.
Putting $x = 0$ in $y = - \dfrac{1}{6}x + 6$, we will then get $y = 6$.
So, the $y$ – intercept of the given line is 6.
Let us put in $y = 0$ in the equation $y = - \dfrac{1}{6}x + 6$ to find the $x$ – intercept.
Putting $y = 0$ in $y = - \dfrac{1}{6}x + 6$, we will then get $- 6 = - \dfrac{1}{6}x$.
Multiplying by – 6, we will then obtain the following:-
$\Rightarrow x = 36$
So, the $x$ – intercept of the given line is 36.
Thus, we have the final answer as follows:-
The slope of the given line $y = - \dfrac{1}{6}x + 6$ is $- \dfrac{1}{6}$.
The $x$ - intercept and the $y$ – intercept of the given line $y = - \dfrac{1}{6}x + 6$ is 6 and 36 respectively.

Note: The students must note that the $x$ and $y$ intercepts basically refer to the points where the line cuts the $x$ – axis and $y$ – axis at. The point where the coordinate axis cut the line at $x$ – axis is $x$ – intercept and $y$ – axis is $y$ – intercept.
The students must also know that the slope of a line is basically the tangent of the angle the line makes with the positive $x$ – axis. Here, in this question, we have tangent of the angle the given line is making with positive $x$ – axis is $- \dfrac{1}{6}$.