Question

How do you find the slope and intercept of \[ - 2x + 3y - 6 = 0\]?

Answer 1

Hint: Using the equation of line, we find the slope of the line. Comparing the equation of a given line to the general equation of line we write the value of slope.
* General equation of the line is \[y = mx + c\] where m is the slope of the line.
* Intercept means the point where the line crosses the respective axis.

Complete step-by-step answer:
We have the equation of line \[ - 2x + 3y - 6 = 0\].
SLOPE OF EQUATION:
We write the equation similar to the general equation of line i.e. in such a way that ‘y’ comes at one side of the equation.
Shift all values except 3y to right hand side of the equation
\[ \Rightarrow 3y = 2x + 6\]
Divide both sides of the equation by 3
\[ \Rightarrow \dfrac{{3y}}{3} = \dfrac{{2x + 6}}{3}\]
Cancel same factors from numerator and denominator on both sides of the equation
\[ \Rightarrow y = \dfrac{2}{3}x + 2\]
Now we compare the equation of line with the general equation of line i.e.\[y = mx + c\].
We get the value of slope i.e. \[m = \dfrac{2}{3}\].
INTERCEPT OF LINE:
Since we know that x-intercept means the point on x-axis where the line cuts the axis and y-intercept means the point on y-axis where the line cuts the y-axis, we will equate the equation of line to 0 and calculate the values of intercepts.
Since the equation of line is the slope intercept form of the equation i.e. m is the slope and c is the y-intercept, and we can write the equation given in slope intercept form i.e. \[y = \dfrac{2}{3}x + 2\]
Then on comparison we can write the value of y-intercept as 2.

\[\therefore \]Slope of the line \[ - 2x + 3y - 6 = 0\] is \[\dfrac{2}{3}\] and the y-intercept is 2.

Note:
Students are likely to make mistakes while shifting the values from one side of the equation to another side of the equation as they forget to change the sign of the value shifted. Keep in mind we always change the sign of the value from positive to negative and vice versa when shifting values from one side of the equation to another side of the equation.