Question

Write the equation of the line parallel to 4x - 5y=12 and passing through the point (5, 7).

Answer 1

y = (4/5)x + 3

Step-by-step explanation:

First, we need to identify the slope of 4x - 5y = 12. To identify the slope we need to solve the equation for y as:

`\begin{gathered} 4x-5y=12 \\ -5y=12-4x \\ y=(12-4x)/(-5) \\ y=(-12)/(5)+(4)/(5)x \end{gathered}`

Since 4/5 is the number beside the x, 4/5 is the slope of the line.

Now, two lines are parallel if they have the same slope, so the slope of our equation will be 4/5.

Then, the equation of a line with slope m that passes through the point (x1, y1) is:

`y-y_1=m(x-x_1)`

So, replacing m by 4/5 and (x1, y1) by (5, 7), we get:

`y-7=(4)/(5)(x-5)`

Finally, solving for y, we get:

`\begin{gathered} y-7=(4)/(5)x-(4)/(5)\cdot5 \\ y-7=(4)/(5)x-4 \\ y=(4)/(5)x-4+7 \\ y=(4)/(5)x+3 \end{gathered}`

Therefore, the equation of the line is:

y = (4/5)x + 3