Question

How do you put the equation $ 2y - 3x = 5 $ into slope intercept form, and graph equation?

Answer 1

Hint:
According to the given question, we have to put the equation $ 2y - 3x = 5 $ into slope intercept form, and graph equation.
So, first of all we have to convert the given equation into the standard slope intercept form of an equation as mentioned below.
Slope- intercept form of an equation: The slope-intercept form is probably the most frequently used way to express equation of line. In general, the slope-intercept form assumes the formula as $ y = mx + c $ , where $ m $ is slope of the line and $ c $ is the y-intercept.
Now, we have to find the x-intercept of the given equation of line to draw the graph of the line, by putting $ y = 0 $ in the given equation of line.

Complete step by step answer:
Step 1: First of all we have to convert the given equation into the standard slope intercept form of an equation as $ y = mx + c $ , mentioned in the solution hint.
So, first of all we have to take $ 3x $ to the R.H.S. of the given equation of line as mentioned below,
 $ \Rightarrow 2y = 5 + 3x $
Step 2: Now, we have to divide by 2 to the L.H.S and R.H.S term of the expression as obtained in the solution step 1.
 $ \Rightarrow \dfrac{{2y}}{2} = \dfrac{{5 + 3x}}{2} $
Now, we have to solve the above expression,
 $ \Rightarrow y = \dfrac{3}{2}\left( x \right) + \dfrac{5}{2} $
Step 3: So, we can see that the expression obtain in the solution step 2 is in the form $ y = mx + c $ ,
Where, $ \dfrac{3}{2} $ is the slope of the linear equation and $ \dfrac{5}{2} $ is the y-intercept of the line.
Step 4: Now, we have to find the x-intercept of the given equation of line to draw the graph of the line, by putting $ y = 0 $ in the given equation of line.
 $
   \Rightarrow 2\left( 0 \right) - 3x = 5 \\
   \Rightarrow - 3x = 5 \\
   \Rightarrow x = \dfrac{{ - 5}}{3} \\
  $
So, we have to find the x-intercept on the line $ = \left( { - \dfrac{5}{3},0} \right) $ and x-intercept on the line $ = \left( {0,\dfrac{5}{2}} \right) $
Final solution: Hence, we put the equation $ 2y - 3x = 5 $ into slope intercept form as $ y = \dfrac{3}{2}\left( x \right) + \dfrac{5}{2} $ .

Note:
It is necessary to understand the slope- intercept form of an equation as mentioned in the solution hint for converting the given equation.
It is necessary to find the x-intercept of the given equation of line to draw the graph of the line, by putting $ y = 0 $ in the given equation of line.