To calculate the slope of the line given by the equation [tex]\(9x - 3y = 15\)[/tex], we need to rewrite the equation in the slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope.
Here's a step-by-step solution:
1. Start with the given equation:
[tex]\[
9x - 3y = 15
\][/tex]
2. We want to solve this equation for [tex]\(y\)[/tex]. To isolate [tex]\(y\)[/tex], we first move the term involving [tex]\(x\)[/tex] to the other side of the equation:
[tex]\[
-3y = -9x + 15
\][/tex]
3. Next, we need to isolate [tex]\(y\)[/tex] completely. To do this, divide every term in the equation by [tex]\(-3\)[/tex]:
[tex]\[
\frac{-3y}{-3} = \frac{-9x}{-3} + \frac{15}{-3}
\][/tex]
4. Simplify each term:
[tex]\[
y = 3x - 5
\][/tex]
5. The equation is now in the slope-intercept form [tex]\(y = 3x - 5\)[/tex]. Comparing this with the general form [tex]\(y = mx + b\)[/tex], we can identify the slope [tex]\(m\)[/tex].
The slope [tex]\(m\)[/tex] of the line is:
[tex]\[
m = 3
\][/tex]
So, the correct answer is:
[tex]\[
3
\][/tex]
