Question

What is an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35?

Answer 1

4x - 5y = 10

Explanation:

We can use the point-slope form to find the line equation:

`\displaystyle{y - y_1 = m(x - x_1)}`

Where (x1,y1) is the point that the line intersects and m is slope. We know the line passes through (-5,-6) and the slope is parallel to the line 4x - 5y = 35. Meaning the slope of that line is equal to slope of 4x - 5y = 35.

In this equation form Ax + By = C, we can find slope by m = - A/B. Therefore, m = -4/-5 which equals to 4/5. Hence, the slope is 4/5

`\displaystyle{y - y_1 = (4)/(5)(x - x_1)}`

And also it intersects the point (-5,-6). Therefore:

`\displaystyle{y - ( - 6) = (4)/(5)(x - ( - 5))} \\ \\ \displaystyle{y + 6 = (4)/(5)(x + 5)}`

Then convert to Ax + By = C to match with the given equation in problem:

`\displaystyle{5(y + 6 )= 5 \left((4)/(5)(x + 5) \right)} \\ \\ \displaystyle{5y + 30 = 4(x + 5)} \\ \\ \displaystyle{5y + 30 = 4x + 20} \\ \\ \displaystyle{ \therefore 4x - 5y = 10}`