Final answer:
To find the equation of a line parallel to y = 1/2x - 7, we keep the same slope of 1/2 and apply the point (-3, -2) to the point-slope form. This process results in the equation y = 1/2x - 2, which is option b.
Step-by-step explanation:
To find an equation in point-slope form for a line parallel to an existing line and passing through a given point, you only need to extract the slope from the original line and use the coordinates of the given point. The original equation is y = ½x - 7, which has a slope (m) of ½. A parallel line will have the same slope.
Now, to write the equation for the new line that passes through the point (-3, -2), we use the point-slope form which is y - y₁ = m(x - x₁), where (x₁, y₁) is the point the line passes through and m is the slope. Substituting the point and the slope, we get: y - (-2) = ½(x - (-3)), which simplifies to y + 2 = ½(x + 3).
Multiplying through by 2 to eliminate the fraction, we get 2y + 4 = x + 3. Subtracting 3 from both sides gives us 2y + 1 = x, and dividing by 2 gives y = ½x - ½. Converting this to y = mx + b form, we find the corresponding y-intercept (b) by substituting x = 0, we find that b = -0.5 - 1.5 which gives us -2. So the correct equation is y = ½x - 2, which corresponds to option b.