Question

What is the equation of line that has a $y$ intercept of 6 and slope of $ - 2$?

Answer 1

Hint: We have to find the equation of straight line. Now, the standard equation of a straight line is $ax + by = c$ . Now, we are given the values of slope and y-intercept. So, we will use the slope intercept form that is $y = mx + c$, to find the equation of this line.

Complete step-by-step solution:
In this question, we are given the value of y intercept and the slope of a line and we are supposed to find the equation of this line.
Now, the standard form of equation of line is: $ax + by = c$- - - - - - - - - - - (1)
So, we have to obtain the equation of the given line in above form.
Now, the slope intercept form equation of line is given by: $y = mx + c$- - - - - - - - (2)
Where, $m = slope$ and $c = $ y – intercept.
In our question, we have the value of slope as $ - 2$ and the value of y – intercept as $6$.
Therefore, $m = - 2$ and $c = 6$.
Putting these values in equation (2), we get
$\Rightarrow y = - 2x + 6$
Now, solving the above equation we get,
$
\Rightarrow 2x + y - 6 = 0 \\
\Rightarrow 2x + y = 6 \\
 $
Hence, the equation of the line having slope $ - 2$ and y – intercept $6$ is $2x + y = 6$.

Note: One of the other important forms of straight line is the intercept form. It is represented by
$\Rightarrow \dfrac{x}{a} + \dfrac{y}{b} = 1$, where a is the x-intercept and b is the y-intercept. It is known as the intercept form because a and b represents the intercepts of the line.