To find the slope of a line parallel to the given equation [tex]\(3x + y = 15\)[/tex], follow these steps:
1. Rewrite the Equation in Slope-Intercept Form:
The standard form of a linear equation is [tex]\(Ax + By = C\)[/tex]. Here, we have the equation given as [tex]\(3x + y = 15\)[/tex]. To find the slope, it is useful to rewrite this equation in the slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope.
2. Isolate [tex]\(y\)[/tex]:
Rearrange the equation to solve for [tex]\(y\)[/tex]:
[tex]\[
3x + y = 15
\][/tex]
Subtract [tex]\(3x\)[/tex] from both sides:
[tex]\[
y = -3x + 15
\][/tex]
3. Identify the Slope:
In the equation [tex]\(y = -3x + 15\)[/tex], the coefficient of [tex]\(x\)[/tex] is the slope [tex]\(m\)[/tex]. Therefore, the slope [tex]\(m\)[/tex] is [tex]\(-3\)[/tex].
4. Find the Slope of the Parallel Line:
The slope of a line parallel to another line is the same as the slope of the given line. Since the slope of the given line [tex]\(y = -3x + 15\)[/tex] is [tex]\(-3\)[/tex], any line parallel to this line will also have a slope of [tex]\(-3\)[/tex].
Thus, the slope of a line parallel to the given line [tex]\(3x + y = 15\)[/tex] is [tex]\(-3\)[/tex].
The correct answer is:
[tex]\[
-3
\][/tex]
