Given the equation of a line as \(3x - 4y = 8\), find the slope of a line parallel to this line.
Answer
Because parallel lines have the same slope, the slope of the line parallel to the given line is also \(\frac{3}{4}\)
Step 1 ：Firstly, we need to convert the given equation into slope-intercept form (\(y = mx + b\)), where \(m\) is the slope. For the equation \(3x - 4y = 8\), we solve for \(y\) to get it in the slope-intercept form
Step 2 ：Subtract \(3x\) from both sides to get \(-4y = -3x + 8\)
Step 3 ：Then, divide both sides by \(-4\) to solve for \(y\), we get \(y = \frac{3}{4}x - 2\)
Step 4 ：From the slope-intercept form, we can see that the slope of the given line is \(\frac{3}{4}\)
Step 5 ：Because parallel lines have the same slope, the slope of the line parallel to the given line is also \(\frac{3}{4}\)
