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Find the slope and intercept of $3x - 2y = 9$?

Last updated date: 24th Jul 2024
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Hint:We know the equation of a line passing through a point and having a slope ‘m’ and with ‘y’ intercept as ‘c’ is given by $y = mx + c$. Here, (x, y) is a variable. We convert the given equation to the slope intercept form. Then comparing the simplified equation with the equation of slope intercept we will get the desired result.

Complete step by step solution:
In the given problem, we are required to find the slope and intercept of the line whose equation is given to us as $3x - 2y = 9$.
The slope intercept form of the equation of a line is $y = mx + c$ where slope of line is given by ‘m’ and y-intercept is given by ‘c’.
So, $3x - 2y = 9$
Shifting term consisting y to right side of the equation,
$\Rightarrow 3x = 9 + 2y$
$\Rightarrow 2y = 3x - 9$
Isolating y so as to convert the equation of line to slope and intercept form, we get,
$\Rightarrow y = \left( {\dfrac{{3x - 9}}{2}} \right)$
Now, we can directly start comparing the equation of the given line with the slope and intercept form of a line and get the values of slope and intercept of the line.
Therefore, On comparing the equation of the line given to us and the slope intercept form of the line, we get,
Slope of the line$= m = \dfrac{3}{2}$ and y-intercept$= c = \dfrac{{ - 9}}{2}$.
Note: ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph. In other words the value of ‘y’ at ‘x’ is equal to zero. Hence, the y intercept of a line can also be found by putting the value of x as zero.