To find the slope of the line given by the equation [tex]\(2x - 5y = 9\)[/tex], we need to rearrange the equation into the slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope.
Here are the step-by-step instructions:
1. Start with the original equation:
[tex]\[
2x - 5y = 9
\][/tex]
2. To isolate [tex]\(y\)[/tex], first move the term involving [tex]\(x\)[/tex] to the right side of the equation:
[tex]\[
-5y = -2x + 9
\][/tex]
3. Next, divide every term by [tex]\(-5\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{-2}{-5}x + \frac{9}{-5}
\][/tex]
4. Simplify the fractions:
[tex]\[
y = \left(\frac{2}{5}\right)x - \frac{9}{5}
\][/tex]
In this equation, [tex]\(y = \left(\frac{2}{5}\right)x - \frac{9}{5}\)[/tex], the coefficient of [tex]\(x\)[/tex] is the slope ([tex]\(m\)[/tex]).
Therefore, the slope [tex]\(m\)[/tex] of the line [tex]\(2x - 5y = 9\)[/tex] is [tex]\(\frac{2}{5}\)[/tex], which equals [tex]\(0.4\)[/tex].
