The slope of the given equation [tex]2x-5y=9[/tex] is [tex]m=\frac{2}{5}[/tex]. This is obtained by rewriting the equation into slope-intercept form and compared with the standard slope-intercept form [tex]y=mx+c[/tex].
The equation with a slope and y-intercept is given as [tex]y=mx+c[/tex]
Here, m is the slope of the equation and c is the y-intercept
The slope of a line describes its steepness and direction. it is calculated as "rise over run". That is the ratio of change in y to the change in x i.e.,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given equation is [tex]2x-5y=9[/tex]
Rewriting the equation into slope-intercept form,
[tex]5y=2x-9[/tex]
⇒ [tex]y=\frac{2}{5} x-\frac{9}{5}[/tex]
In comparison with the standard form we get,
Slope, [tex]m=\frac{2}{5}[/tex]
and y-intercept, [tex]c=-\frac{9}{5}[/tex]
Therefore, the slope of the given equation 2x-5y=9 is [tex]m=\frac{2}{5}[/tex].
Learn more about slope-intercept form here:
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