Final answer:
To find the equation of a line parallel to y=2x+5 and passing through the point (2, -4), we use the slope of 2 and solve for the y-intercept 'b' to discover the new equation is y=2x-8.
Step-by-step explanation:
The student has asked for the equation of a line that is parallel to the line described by the equation y=2x+5 and passes through the point (2, -4). To find the equation of a line parallel to another, one must use the same slope, as parallel lines have identical slopes. The initial line equation given, y=2x+5, has a slope (m) of 2. Since the new line must be parallel, its slope will also be 2. The next step involves finding the y-intercept (b) of the new line using the point it passes through, which in this case is (2, -4). By substituting x and y with these values into the slope-intercept form y=mx+b, we get:
- -4 = (2)(2) + b
- -4 = 4 + b
- b = -4 - 4
- b = -8
Therefore, the equation of the line parallel to y=2x+5 and passing through (2, -4) is y=2x-8.