Final answer:
The equation of the line with a slope of 1/2 passing through (-3, 2/3) is y = (1/2)x + 8/3, derived using the point-slope formula and simplifying.
Step-by-step explanation:
The question asks for the equation of a line with a slope of 1/2 that passes through the point (-3, 2/3). To find this equation, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Plugging in our values, the equation becomes: y - 2/3 = 1/2(x + 3). Simplifying, we multiply both sides by 2 to get rid of the fraction: 2y - 4/3 = x + 3. Then, we solve for y to get y = 1/2x + 8/3, which is choice (a).
To find the equation of a line with a given slope and a point on the line, we use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values from the question, we have y - 2/3 = 1/2(x - (-3)). Simplifying, we get y - 2/3 = 1/2x + 3/2. Rearranging the equation, we have y = 1/2x + 3/2 + 2/3. Combining the fractions, we get y = 1/2x + 8/6 + 4/6. Simplifying further, we have y = 1/2x + 12/6. Finally, we can simplify the equation to y = 1/2x + 2.