Question

Find the equation of the line that is parallel to 4x - 8y equals 9 and passes through (-3, 6)​

Answer 1

For this case we have the following equation:

$4x-8y = 9$

We manipulate algebraically to bring the equation to the slope-intersection form y = mx + b

Where:

m: It's the slope

b: It is the cut-off point with the y axis

$8y = 4x-9\\y =\frac {4} {8} x- \frac {9} {8}\\y =\frac {1} {2} x- \frac {9} {8}$

By definition, if two lines are parallel then their slopes are equal.

Thus, the line is of the form:

$y = \frac {1} {2} x + b$

We find the cut-off point by replacing the given point:

$6 = \frac {1} {2} (- 3) + b\\6 = - \frac {3} {2} + b\\b = 6 + \frac {3} {2}\\b = \frac {12 + 3} {2}\\b = \frac {15} {2}$

Thus, the line is of the form:

$y = \frac {1} {2} x + \frac {15} {2}$

Answer:

$y = \frac {1} {2} x + \frac {15} {2}$