Answer:
y = -2x - 8
Step-by-step explanation:
To find the equation of a line that passes through a given point and is parallel to another line, we can use the fact that parallel lines have the same slope. The given line is in the form 2x + y = 5, and we can rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
First, let's rewrite 2x + y = 5 in slope-intercept form:
y = -2x + 5
Now, we can see that the slope (m) of the given line is -2. Since the line we are looking for is parallel, it will also have a slope of -2.
Now, we use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Let's use the point (-6, 4) and the slope m = -2 in the formula:
y - 4 = -2(x - (-6))
Simplify:
y - 4 = -2(x + 6)
Distribute -2:
y - 4 = -2x - 12
Isolate y:
y = -2x - 12 + 4
Combine like terms:
y = -2x - 8
So, the equation of the line that passes through the point (-6, 4) and is parallel to the line 2x + y = 5 is y = -2x - 8.
