Final answer:
The equation of the line that passes through the points (-5,-8) and (5,4) is found by determining the slope, which is 1.2, and then using one of the given points and the point-slope form to find the equation, resulting in y = 1.2x - 2.
Step-by-step explanation:
To find an equation of a line that passes through the points (-5,-8) and (5,4), we first determine the slope of the line using the slope formula m = (y2 - y1) / (x2 - x1). Substituting the given points into the slope formula, we get m = (4 - (-8)) / (5 - (-5)) = 12 / 10 = 1.2. Therefore, the slope of the line is 1.2.
If we designate the slope as m and one of the points, say (-5, -8), as (x1, y1), we can use the point-slope form of the equation of a line y - y1 = m(x - x1) to find the equation. Plugging in the values, the equation becomes y - (-8) = 1.2(x - (-5)). This simplifies to y + 8 = 1.2x + 6, and by subtracting 8 from both sides, we get the equation in slope-intercept form, y = 1.2x - 2.
We can verify this by ensuring that both original points satisfy the equation. For the point (-5, -8): y = 1.2(-5) - 2 = -6 - 2 = -8, which matches the y-value of the point. Similarly, for the point (5, 4): y = 1.2(5) - 2 = 6 - 2 = 4, which also matches the y-value of the point. Therefore, the equation y = 1.2x - 2 is the correct equation of the line passing through the points (-5, -8) and (5, 4).