When lines are parallel, they have the same slope. Therefore, we will start by finding the slope of the given line. To do so, consider the given graph.
Looking at the graph, we can say that the slope of the given line is - 2. All lines that are parallel to the given line have a slope of - 2.
We can write a general equation in slope-intercept form for these lines.
y= - 2x+ b
We are asked to write the equation of a line parallel to the given line that passes through the point ( 5, - 8). By substituting this point into the above equation for x and y, we will be able to solve for the y-intercept b of the parallel line.
Now that we have the y-intercept, we can write the parallel line to the line at the graph through (5,- 8).
y= - 2x+ 2 ⇔ y + 2x = 2
This corresponds to option G.
