Final answer:
The equation of a line that is parallel to 6x-3=-4 and passes through (4,3) is y = 6x - 21. This is derived by maintaining the slope of the original line, which is 6, and using the point-slope form equation with the given point.
Step-by-step explanation:
To find the equation of a line that is parallel to the given line 6x-3=-4 and passes through the point (4,3), we need to use the concept of slope. The original line can be rearranged into slope-intercept form (y = mx + b) to reveal its slope. Rearranging 6x-3=-4 gives us y = 6x + 1, which has a slope of 6. A line that is parallel will have the same slope.
To find the equation of our new line, we use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Substituting our point (4,3) and the slope of 6 into this formula, we get y - 3 = 6(x - 4).
Expanding this out gives us the final equation of the line that is parallel to the given line and passes through the point (4,3): y = 6x - 21.