By using the intercept method how do you find the equations of straight line passing through (-3,0) and (0,2).

Hint: For finding the equation of line, when we have the x and y intercept we can use the intercept formula \[\dfrac{x}{a}+\dfrac{y}{b}=1\] and then substitute the x and y intercept in the formula and we will get the equation of the line that was required in the question:

Complete step by step solution:
The points that has been stated are (-3,0) and (0,2)
From the points that have been stated above we can find the x and y intercept
X-intercept: we can find the x-intercept when the value of y=0 so we can also say that x-intercept is -3.
Y-intercept: we can find the y-intercept when the value of x=0 so we can also say that y-intercept is 2.
After finding the x-intercept and y-intercept we can use the intercept formula which is stated as below
\[\dfrac{x}{a}+\dfrac{y}{b}=1\]
Where we can say that
a: x-intercept
b: y-intercept
We can now substitute the x-intercept and y-intercept, so we get
a = -3 and b = 2
now we can substitute the values of a and b in the intercept equation and we get:
\[\begin{align}
  & \Rightarrow \dfrac{x}{-3}+\dfrac{y}{2}=1 \\
 & \\
\end{align}\]
Now so as to simplify the given equation we will take the LCM of -3 and 2 and we find the LCM to be 6.
Now we will multiply both LHS and RHS by 6 so as to remove the denominator on the LHS side of the equation and we get:
\[\begin{align}
  & \Rightarrow (\dfrac{x}{-3}+\dfrac{y}{2})6=1(6) \\
 & \Rightarrow \dfrac{6x}{-3}+\dfrac{6y}{2}=6 \\
 & \Rightarrow -2x+3y=6 \\
 & \Rightarrow 3y=2x+6 \\
 & \Rightarrow y=\dfrac{2}{3}x+\dfrac{6}{3} \\
 & \Rightarrow y=\dfrac{2}{3}x+2 \\
\end{align}\]
So from the above solved equations we can say that the final equation of line is \[y=\dfrac{2}{3}x+2\]

Note:
There are some general mistakes that happen in how to take the x and y intercept. To find the x-intercept take the value of y=0 and the respective value of x is the x-intercept. The same is with y-intercept i.e. put x=0 and the respective value of y is y-intercept.