Final answer:
To find the point-slope equation for a line parallel to 4x - 2y = 9 with an x-intercept of (4,0), we determine the slope of the given line, which is 2. Using the point-slope form, we substitute the slope and coordinates of the x-intercept to obtain the equation y = 2x - 8.
Step-by-step explanation:
To find the point-slope equation for a line parallel to 4x - 2y = 9, we need to determine the slope of the given line. We can rearrange the equation into slope-intercept form, y = mx + b, where m is the slope. Subtracting 4x from both sides and dividing by -2, we get y = 2x - 9. This tells us that the slope of the given line is 2.
Since we want to find the point-slope equation for a line parallel to the given line, the slope of the new line will also be 2. We know that the x-intercept of the new line is (4,0). To find the equation, we use the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values into the equation, we get y - 0 = 2(x - 4), which simplifies to y = 2x - 8. Therefore, the point-slope equation for the line parallel to 4x - 2y = 9 with an x-intercept of (4,0) is y = 2x - 8.