Equation of a line (point/point of intersection)

You can view as many worked out examples as you want. First you are shown the question. Click Show Answer to view the answer.
Click Show another Example to view another example. The best way to master mathematics is by practice. But practice requires time.
If you don't have the time to practice, you can always view many practice problems completely worked out and become good at it too.

Find the equation of the line passsing through the point P $\left(\frac{5}{7},3\right)$ and the intersection of the lines $8x+8y-1= 0$ and $6x-9y+1= 0$

**Answer**

The lines $8x+8y-1= 0$ and $6x-9y+1= 0$ intersect at the point Q$\left(\frac{-1}{120},\frac{-7}{60}\right)$

The given line passes through the point P $\left(\frac{5}{7},3\right)$ and $\left(\frac{-1}{120},\frac{-7}{60}\right)$

The slope of the line joining the points $P\left(\frac{5}{7},3\right)$ and $Q\left(\frac{-1}{120},\frac{-7}{60}\right)$ is given by $m=\frac{\frac{-7}{60}-3}{\frac{-1}{120}-\frac{5}{7}}=\frac{2618}{607}$

The equation of the line is$$y - y_0 = m\left(x - x_0\right)$$

or, $$y= mx + y_0-mx_0$$

Substituting the values of $m$, $x_0$ and $y_0$, we get

$y =\frac{2618}{607}x+3-\left(\frac{2618}{607}\right)\left(\frac{5}{7}\right)$

or, $y =\frac{2618}{607}x+3-\frac{1870}{607}$

or, $y=\frac{2618}{607}x-\frac{49}{607}$