Question

How do you change the equation 2x – 6y = 5 from standard to point slope and slope intercept?

Answer 1

Hint: Since, the given equation is given in a standard form, we need to divide the equation by coefficient of y and keep the rest of the terms to the other side of equal sign. After that compare it with equation y = mx + c and get the desired values.

Complete step by step solution:
To clear any doubt in this, we are going to use the equation of a line. It is y = mx + c. Here, m is the point slope and c is the y intercept.
Now, we will consider the equation 2x – 6y = 5. We will take 2x to the right side of the equation. This gives, – 6y = 5 – 2x. After this we will divide the whole equation by – 6. Thus, we get
$\begin{align}
  & \Rightarrow \dfrac{-6y}{-6}=\dfrac{5}{-6}-\dfrac{2x}{-6} \\
 & \Rightarrow y=\dfrac{1}{3}x-\dfrac{5}{6} \\
\end{align}$
By comparing it with y = mx + c we can have the value of $m=\dfrac{1}{3}$ and $c=-\dfrac{5}{6}$. Here, m is the slope point and y is the slope intercept.
Hence, the slope point and the slope intercept are $m=\dfrac{1}{3}$ and $c=-\dfrac{5}{6}$ respectively.

Note: One should not get confused by the term intercept. As the equation can give the value of x instead of y but then in this case, the value of x will not be considered as a slope intercept. In order to get the right answer we need to take the help of the equation of line y = mx + c. The easiest way to simplify the given equation is to divide it by the coefficient of y and get the correct value of m and y-intercept. By the term point slope, we mean a slope over a particular point, say $\left( {{x}_{1}},{{y}_{1}} \right)$. The slope is represented by m and its value is gained by $m=\dfrac{y-{{y}_{1}}}{x-{{x}_{1}}}$. Moreover, the slope intercept is the intercept means the coefficient of y.