Final answer:
Using the slope formula and point-slope form, the linear equation that represents the line containing the points (-6,-8) and (3,-2) is found to be y = 2/3x - 4. Therefore, the correct answer is option C.
Step-by-step explanation:
To find the equation of a line that passes through the given points (-6,-8) and (3,-2), we first need to calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the points into the formula, we get m = (-2 - (-8)) / (3 - (-6)) = 6 / 9, which simplifies to 2 / 3. Using the slope and one of the points, we can then apply the point-slope form of the equation of a line, which is y - y1 = m(x - x1), to create the equation.
Using point (3, -2) and slope 2/3, the equation becomes y - (-2) = 2/3 (x - 3), which simplifies to y + 2 = 2/3 (x - 3). From the given options, none of them directly match this form, but we can convert it to slope-intercept form, which is y = mx + b, to compare with the answers provided.
Expanding the equation gives us y = 2/3 x - 2 - 2, which simplifies to y = 2/3x - 4. Comparing this with the options given, option C is the correct equation representing a line through the points (-6, -8) and (3, -2).