What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line 5x+4y=165x+4y=16?

The equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 is  

Step-by-step explanation:

We need to write an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16.

The equation will be of form where m is slope and b is y-intercept.

Finding slope of the line:

Since both the lines are parallel, and we know that parallel lines have same slope.

The slope of given line can be found by writing in slope-intercept form

Comparing with the slope m is:

So, the slope of required line is:

Now, finding y-intercept b

y-intercept can be found using slope and point (8,-7)

So, we get y-intercept: b=3

Now, the equation of required line having slope and y-intercept b=3 is:

So, the equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16