Consider the line with the equation: $y=\frac{3}{5} x-8$
Give the equation of the line parallel to Line 1 which passes through $(10,4)$ :
Give the equation of the line perpendicular to Line 1 which passes through $(10,4)$ :
Check Answer

Step 1 ：The slope of a line parallel to a given line is the same as the slope of the given line. In this case, the slope of the given line is \(\frac{3}{5}\). So, the slope of the line parallel to the given line is also \(\frac{3}{5}\).

Step 2 ：The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. In this case, the negative reciprocal of \(\frac{3}{5}\) is \(-\frac{5}{3}\).

Step 3 ：The equation of a line in slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We can find the y-intercept by substituting the coordinates of the given point and the slope into this equation and solving for \(b\).

Step 4 ：For the parallel line, substituting \(m = \frac{3}{5}\), \(x = 10\), and \(y = 4\) into the equation \(y = mx + b\) and solving for \(b\), we get \(b = -2\).

Step 5 ：For the perpendicular line, substituting \(m = -\frac{5}{3}\), \(x = 10\), and \(y = 4\) into the equation \(y = mx + b\) and solving for \(b\), we get \(b \approx 20.67\).

Step 6 ：Now that we have the slopes and y-intercepts of the lines parallel and perpendicular to the given line, we can write their equations in slope-intercept form.

Step 7 ：\(\boxed{\text{Final Answer: The equation of the line parallel to Line 1 which passes through }(10,4)\text{ is }y = \frac{3}{5}x - 2\text{ and the equation of the line perpendicular to Line 1 which passes through }(10,4)\text{ is }y = -\frac{5}{3}x + 20.67}\)