Sure, let's solve this step-by-step.
Step 1: Identify the points.
In our case, we have two points given. Let's denote them as point1(-2, 4) and point2(10, -2).
Step 2: Find the slope of the line.
The slope of a line passing through points (x1, y1) and (x2, y2) is given by the formula (y2 - y1)/(x2 - x1).
So here, substituting the values into the formula, we find:
Slope m = ( -2 - 4 ) / ( 10 - (-2)) = -6 / 12 = -0.5
Hence, the slope of the line is -0.5.
Step 3: Write down the equation of the line.
The formula to describe a line with slope m passing through the point (x1, y1) is y - y1 = m(x - x1).
Substituting m = -0.5, x1 = -2, and y1 = 4,
We obtain:
y - 4 = -0.5(x + 2)
So, the equation of the line in point-slope form is y - 4 = -0.5(x + 2).
Comparing with the options, we see that option a) matches our answer. Therefore, the correct answer to this question should be option a) - Slope = -0.5, Equation: y - 4 = -0.5(x + 2).
Answer: a) Slope = -0.5; Equation: y - 4 = -0.5(x + 2)