Answer:
y = 5/2x + 4
Explanation:
Relationship between the slopes of parallel lines:
- The slopes of parallel lines are equal to each other.
- This means that once we find the slope of 5x - 2y = 2, we'll also have the slope of the other line.
Identifying the form of 5x - 2y = 2:
The equation 5x - 2y = 2 shows the standard form of a line, whose general equation is given by:
Ax + By = C, where:
- A, B, and C are constants.
We can easily find the slope of 5x - 2y = 2 by converting it to the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where:
- m is the slope,
- and b is the y-intercept.
Converting 5x - 2y = 2 to slope-intercept form and identifying the slope:
Thus, we isolate y in 5x - 2y = 2 to find the slope of this line and the other line:
(5x - 2y = 2) - 5x
(-2y = -5x + 2) / -2
y = 5/2x - 1
Therefore, 5/2 is the slope of 5x - 2y = 2 and the other line.
Finding the y-intercept (b) of the other line and writing the equation of the line (in slope-intercept form):
Now, we can find the y-intercept of the other line by substituting 5/2 for m and (-4, -6) for b in the general equation of the slope-intercept form:
-6 = 5/2(-4) + b
-6 = -20/2 + b
(-6 = -10 + b) + 10
4 = b
Thus, the y-intercept of the line is 4.
Therefore, y = 5/2x + 4 is the equation of the line that passes through (4, -6) and is parallel to the line 5x - 2y = 2.