Answer:
[tex]y=-2.5x-9[/tex]
Step-by-step explanation:
One is given the following equation.
[tex]5x + 2y = 12[/tex]
The problem asks one to find a line that is parallel to this one, and passes through the point: [tex](-2, 4)[/tex]. The equation of the given line is in the standard format. The easiest approach to solve this problem is to change the equation of the given line into the slope-intercept format. The solve intercept format follows the following general equation:
[tex]y=mx+b[/tex]
Where (m) is the slope of the line and (b) is the y-intercept. Manipulate the given equation such that it follows this format:
[tex]5x+2y=12\\2y=12-5x\\y=6-2.5x\\\\y=-2.5x+6[/tex]
One property of parallel lines is that they have the same slope. Therefore, if one uses the slope-intercept format to represent the slope of the parallel line, then one can state the following:
[tex]y=-2.5x+b[/tex]
Substitute a given point on this line ([tex]-2,4[/tex]) , and solve for (b) to find (b):
[tex]y=-2.5x+b\\(4)=-2.5(-2)+b[/tex]
Simplify,
[tex]4=-2.5(-2)+b\\-4=5+b[/tex]
Inverse operations,
[tex]-4=5+b\\-9=b[/tex]
Substitute this back into the equation in slope-intercept form to find the equation of the parallel line:
[tex]y=-2.5x-9[/tex]
