Final answer:
The equations of lines that are parallel to the line y = 2x - 3 are B. y = 2x - 1, C. 2x - y = 5, and E. 4y + 3 = 8x, as they all have the same slope of 2.
Step-by-step explanation:
To determine which of the given equations are parallel to the original equation y = 2x - 3, we need to compare the slopes of each equation. Parallel lines have the same slope (m) but can have different y-intercepts (b). The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
The original equation has a slope of 2. Now let's look at each option to find lines with the same slope:
- A. y = 2 - This is a horizontal line with a slope of 0, not parallel to the original line.
- B. y = 2x - 1 - This has a slope of 2, the same as the original line, so it is parallel.
- C. 2x - y = 5 - If we rearrange it to slope-intercept form, we get y = 2x - 5, which also has a slope of 2, making it parallel to the original line.
- D. 3x + 2y = 7 - Rearranged into slope-intercept form as y = -1.5x + 3.5, it has a slope of -1.5, which is not parallel to the original line.
- E. 4y + 3 = 8x - Rearranged to y = 2x - 0.75, this too has a slope of 2, and therefore is parallel to the original line.
Therefore, the equations of lines that are parallel to the original line are B, C, and E.