To determine the slope of a line parallel to the line given by the equation [tex]\(5y + 7x = 12\)[/tex], we first need to rewrite the equation in slope-intercept form, [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope.
Here are the steps to convert the equation [tex]\(5y + 7x = 12\)[/tex] into slope-intercept form:
1. Isolate [tex]\(y\)[/tex] on one side of the equation:
[tex]\[
5y + 7x = 12
\][/tex]
Subtract [tex]\(7x\)[/tex] from both sides to get:
[tex]\[
5y = -7x + 12
\][/tex]
2. Solve for [tex]\(y\)[/tex] by dividing every term by 5:
[tex]\[
y = \frac{-7}{5}x + \frac{12}{5}
\][/tex]
In the equation [tex]\(y = \frac{-7}{5}x + \frac{12}{5}\)[/tex], the coefficient of [tex]\(x\)[/tex] is the slope.
3. Identify the slope:
The coefficient of [tex]\(x\)[/tex] here is [tex]\(\frac{-7}{5}\)[/tex].
Therefore, the slope of the line [tex]\(5y + 7x = 12\)[/tex] is [tex]\(-\frac{7}{5}\)[/tex].
4. Slope of the parallel line:
Since parallel lines have the same slope, any line that is parallel to the line [tex]\(5y + 7x = 12\)[/tex] will also have a slope of [tex]\(-\frac{7}{5}\)[/tex].
The answer is:
(B) [tex]\(m = -\frac{7}{5}\)[/tex].
