Final answer:
None of the answer options matches the correct equation of the line through the points (3, -8) and (6, -4). The correct equation is y = (4/3)x minus 12.
Step-by-step explanation:
Completing the Equation of the Line. To complete the equation of the line through the points (3, -8) and (6, -4), we first need to find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula gives us m = (-4 - (-8)) / (6 - 3) = 4 / 3. Now, using the slope-point form of the equation y - y1 = m(x - x1) and substituting one of the points (3, -8), we get y - (-8) = (4 / 3)(x - 3). Simplifying, we find the equation y = (4 / 3)x - 4 - 8. Further simplification results in y = (4 / 3)x - 12, which can also be written as y = 4x/3 - 12. Therefore, none of the options given (a) through (d) correctly represent the equation of the line through the given points.
Each of the incorrect answer options does not match the slope we calculated or the correct y-intercept of the line. It's important to correctly calculate both the slope and the y-intercept when writing the equation of a line. To find the equation of the line passing through the points (3, -8) and (6, -4), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. First, we need to find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the points (3, -8) and (6, -4) into the formula, we get: m = (-4 - -8) / (6 - 3) = 4 / 3. Next, we can choose any of the given options and substitute the slope (m) and the coordinates of one of the points (3, -8) into the equation. Checking each option, we find that option b) y = 2x + 2 satisfies the equation y = 2x + 2 when x = 3 and y = -8. Therefore, the correct answer is b) y = 2x + 2.