Final answer:
To find a parallel line's equation, identify the slope from the original equation (m=-2), and then apply the point (3, 1) to determine the y-intercept. The correct equation in slope-intercept form is y = -2x + 7, corresponding to option b.
Step-by-step explanation:
The slope-intercept form of a linear equation is typically written as y = mx + b, where m represents the slope of the line and b represents the y-intercept. To find an equation for a line that is parallel to another, we need to ensure that the slopes are identical, as parallel lines have the same slope. The equation 4x + 2y = 10 can be rewritten in slope-intercept form by solving for y to find the slope.
The adjusted form is y = -2x + 5 which indicates a slope of -2. A line parallel to this must also have a slope of -2. Substituting the point (3, 1) into the slope-intercept form and solving for b yields the equation y = -2x + 7, confirming that option d, y = 2x + 7, is incorrect and the correct answer is option b, which is y = -2x + 7.