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What is the slope of the line given by the equation [tex]2x - 5y = 9[/tex]?

Sagot :

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].