Final answer:
To find the equation of a line parallel to y=5x-1 that goes through (3, 5), we match the slope (5) and use the point to solve for the y-intercept, resulting in the equation y = 5x - 10.
Step-by-step explanation:
The given equation y=5x-1 represents a line with a slope of 5. Any line parallel to this one must have the same slope. We are seeking an equation for a line that passes through the point (3, 5) and is parallel to the given line, thus it will have the same slope of 5. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
To find the y-intercept of the new line, we use the point (3, 5) and the slope of 5 in the slope-intercept form of the equation:
- Substitute the slope (m=5) and the coordinates of the point into the equation: 5 = 5(3) + b.
- Solve for b by simplifying the equation: 5 = 15 + b.
- Subtract 15 from both sides to find b: b = 5 - 15.
- Therefore, b = -10.
- The equation of the line is y = 5x - 10.
So, the correct answer is b) y = 5x - 10.