For two lines to be parallel, their slope must be the same.
To find the slope, we can use the form: [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]
For the top line, the change in height (y value) can be seen as a - 0 or simply a, and the change in base is just -b (because our [tex]x_1[/tex] is just 0, from the origin.
Hence, line 1's gradient is: [tex]-\frac{a}{b}[/tex]
Now, we can repeat this process for line 2:
Change in height is -d, change in base is c
Hence, line 2's gradient is: [tex]-\frac{d}{c}[/tex]
For the two lines to be parallel, both gradients must be the same:
[tex]-\frac{a}{b} = -\frac{d}{c}[/tex]
