Answer:
Explanation:
To find the equation of a line that passes through a given point and is parallel to a given line, we can use the fact that parallel lines have the same slope.
First, let's rearrange the equation 5x - 2y = 6 into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
5x - 2y = 6
-2y = -5x + 6
y = (5/2)x - 3
So the given line has a slope of 5/2.
Since the line we want is parallel to this line, it must also have a slope of 5/2. So we can use the point-slope form of a line to write the equation of the line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point that the line passes through. Substituting m = 5/2, x1 = -2, and y1 = -4, we get:
y - (-4) = (5/2)(x - (-2))
Simplifying, we get:
y + 4 = (5/2)(x + 2)
Distributing the 5/2, we get:
y + 4 = (5/2)x + 5
Subtracting 4 from both sides, we get:
y = (5/2)x + 1
So the equation of the line that passes through the point (-2, -4) and is parallel to the line 5x - 2y = 6 is y = (5/2)x + 1.