Question

Write in slope-intercept form an equation of the line that passes through the point (r,p) with slope q
(20 points)

Answer 1

Answer:

y = qx - qp + r

Step-by-step explanation:

Plugging this into the point-slope form, we get (y-r) = q(x-p), which makes y = qx - qp + r.

Answer 2

The slope-intercept form of the line that passes through the point (r,p) with slope q is $\frac{y}{p-qr} +\frac{x}{-(\frac{p-qr}{q} )} = 1$

What is the equation of a straight line?

The equation of a straight line passing through a point (x₁,y₁) and slope m is:

y-y₁ = m(x-x₁)

It is given that

The line passes through the point  (r,p) and the slope is q

Equation of the line will be:

y-p = q(x-r)

y-qx = p-qr....(1)

The slope-intercept form of a line having x and y-intercepts as a and b respectively is:

$\frac{x}{a} + \frac{y}{b} =1$

Divide eq1 by p-qr to get the slope-intercept form

$\frac{y}{p-qr} +\frac{x}{-(\frac{p-qr}{q} )} = 1$

Therefore, the slope-intercept form of the line that passes through the point (r,p) with slope q is $\frac{y}{p-qr} +\frac{x}{-(\frac{p-qr}{q} )} = 1$

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