Question

Find the slope and the y-intercept of the line. $$5 x-5 y=1$$

Short answer

The slope of the line is 1, and the y-intercept is -1/5.

Step-by-step solution

Rearrange the equation in slope-intercept form

To do this, firstly, arrange the terms of the given equation \(5x - 5y = 1\) in order to isolate 'y'. It can be done by subtracting \(5x\) from both sides which results in \(-5y = -5x + 1\). Further, divide each side by -5 to solve for 'y'. This gives us \(y = x - \frac{1}{5} \). So, \(y\) has been expressed as a function of \(x\).

Identify the slope and y-intercept

From the equation \(y = x - \frac{1}{5} \), we can see that it is in the slope-intercept form \(y = mx + b\). The slope \(m\) is the coefficient of \(x\), and in our case it is 1. The y-intercept \(b\) is the constant term, and here it is \(-\frac{1}{5} \).