Final answer:
To find the equation of a line parallel to another line, determine the slope of the given line, and then use the point-slope form of a line to write the equation. The equation of the line parallel to the given line and passing through the point (3, 2) is y = 4x - 10.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a line to write the equation. The given line is 8x = 2y + 4. To find its slope, we need to rearrange the equation to y = mx + b form, where m represents the slope. After rearranging, we have y = 4x - 2. So the slope of the given line is 4.
Since the line we want to find is parallel to the given line, the slopes of the two lines will be equal. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
Using the given point (3, 2) and the slope of 4, we can plug the values into the slope-intercept form to find the equation of the line. The equation would be y = 4x + b. We can substitute the x and y values of the point into this equation to solve for b. Plugging in (3, 2) gives us 2 = 4(3) + b. Solving for b, we get b = -10.
Therefore, the equation of the line parallel to the given line and passing through the point (3, 2) is y = 4x - 10.