Answer:
y = 3/4x + 13/4
Explanation:
Relationship between the slopes of parallel lines:
- The slopes of parallel lines have the same slope.
- This means that identifying the slope of y = 3/4x - 2 will also give us the slope of the other line.
Identifying the slope of y = 3/4x - 2:
The equation y = 3/4x - 2 is in 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.
Thus, the slope of both lines is 3/4.
Finding the y-intercept (b) of the other line:
Now, we can find the y-intercept (b) of the other line by substituting (5, 7) for (x, y) and 3/4 for m in the general equation of the slope-intercept form:
7 = 3/4(5) + b
(7 = 15/4 + b) - 15/4
13/4 = b
Thus, the y-intercept (b) of the other line is 13/4.
Writing the equation of the other line (in slope-intercept form):
Therefore, y = 3/4x + 13/4 is the equation of the line in slope-intercept form.