Find the slope of the line whose equation is px - qy = r + 1.

Solution:

Given, the equation of the line is px - qy = r + 1

We have to find the slope of the line.

We can find the slope of the line in two methods.

1) slope = -\(\frac{coefficient\, of\, x}{coefficient\: of\: y}\)

From the equation px - qy = r + 1

Coefficient of x = p

Coefficient of y = -q

So, slope = -(p/-q)

Slope = p/q

2) The equation of the line in slope-intercept form is given by y = mx + c

Where, m is the slope.

Now, converting the given equation in slope-intercept form,

qy = px - (r + 1)

Dividing by q on both sides,

y = (p/q)x - (r+1)/q

Now, slope, m = p/q

Therefore, the slope of the line is p/q.

---

Find the slope of the line whose equation is px - qy = r + 1.

Summary:

The slope of the line that has the equation px - qy = r + 1 is p/q