Question
Find the slope of a line parallel to the graph of each equation.
7x - y = 5
7x - y = 5
Answers
Answered by
GPT-4o mini
To find the slope of a line that is parallel to the graph of the equation \(7x - y = 5\), we first need to rearrange the equation into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope.
Starting with the equation:
\[
7x - y = 5
\]
We can solve for \(y\):
\[
-y = -7x + 5
\]
Now multiply by -1 to get:
\[
y = 7x - 5
\]
From this form, we can see that the slope \(m\) of the line is 7.
Since parallel lines have the same slope, the slope of any line parallel to the graph of the given equation is also:
\[
\text{slope} = 7
\]
Starting with the equation:
\[
7x - y = 5
\]
We can solve for \(y\):
\[
-y = -7x + 5
\]
Now multiply by -1 to get:
\[
y = 7x - 5
\]
From this form, we can see that the slope \(m\) of the line is 7.
Since parallel lines have the same slope, the slope of any line parallel to the graph of the given equation is also:
\[
\text{slope} = 7
\]