Final answer:
The equation of the straight line passing through the points (-4,-2) and (4,4) is y = 3/4x + 1. None of the provided options a) y = 2x, b) y = x, c) y = -x, d) y = -2x match this equation.
Step-by-step explanation:
To find the equation of the straight line that passes through the points (-4, -2) and (4, 4), we first need to determine the slope of the line. The formula for the slope ('m') is rise divided by the run. In this case, the rise is the change in y-coordinates (4 - (-2)) and the run is the change in x-coordinates (4 - (-4)). Therefore, the slope m is (4 - (-2)) / (4 - (-4)) = 6 / 8 = 3 / 4.
Now that we have the slope, we can use the point-slope form of a line which is:
y - y1 = m(x - x1),
where (x1, y1) is a point on the line, and m is the slope. Substituting one of the points (-4, -2) into the formula, we get:
y - (-2) = 3/4(x - (-4))
Simplifying this we have y + 2 = 3/4x + 3, which gives us y = 3/4x + 1 after subtracting 2 from both sides.
Looking at the options provided by the student, none of them matches the equation y = 3/4x + 1. Thus, if we limit our answer to the provided choices, none of them are correct. However, the equation we derived is the correct linear equation for the given line segment.