Question 653408
To find equation of a line parallel to a given line through a point, the first step is to know a condition of parallel lines.

Two lines are parallel when they have the same slope.

The equation of our given line is 4x - 3y = 7

To find the slope, solve for y:

Start by subtracting 4x from both sides of the equation:

-3y = 7 - 4x

Then divide both sides by -3:

y = -{{{(7/3) + (4/3)x}}}

Recall y = mx + b? which means the slope m is the coefficient of x, so the slope of the given line is {{{4/3}}}

Since two lines have the same slope when they are parallel, then our slope is also {{{4/3}}}. Now we will use slope m and the point given (3, 5) to find the equation using the formula y - y1 = m(x - x1)

y - 5 = {{{4/3}}}(x - 3)

Add 5 to both sides of the equation:

y = {{{4/3}}}(x - 3) + 5

Simplify

y = {{{4/3}}}x - 4 + 5

y = {{{4/3}}}x + 1