Question

How do you write the equation of the line given the slope $2$ , $y$ -intercept $\left( 0,9 \right)$ ?

Answer 1

In problems like this it is necessary to know the slope and $y$ -intercept of the straight line to write an equation of it. We will get the equation in its slope intercept form by using the values of the slope and $y$ -intercept. For that we will take the general equation of a straight line in the slope intercept form and putting the given values in that equation we will get the equation of the straight line.

Complete step by step answer:
To get the equation of a straight line in the slope intercept form it is necessary to know the values of the slope and the y-intercept. In this question we are given the value of the slope of the straight line as 2 and the line passes through the point $\left( 0,9 \right)$ .
As the straight line passes through $\left( 0,9 \right)$ we can say the $y$ -intercept of the line is $9$ as the line cuts the $y$ axis at a distance of $9$ units from the origin.
Now, we take the general equation of the straight line in the slope intercept form as
$y=mx+c$
Here, $m$ is the slope and $c$ is the $y$ -intercept of the straight line
Hence, for this problem we can write $m=2$ and $c=9$
Now, we substitute the above values of the slope and $y$ -intercept in the general equation of the straight line as shown below
$\Rightarrow y=2x+9$

Therefore, we can conclude that the equation of the straight line is $y=2x+9$ .

Note: We must keep in mind that we have taken the value of $c$ as $9$ because the $x$ coordinate of the given point is zero. If we were given a point other than that we should have put that point in the equation of the line to find the value of $c$ . Also, we must put the proper values in the equation that are given, as inaccurate values will lead to wrong answers.