Final answer:
To determine the equation of a line parallel to the line joining points A(-5, -1) and B(3, 8) and passing through C(-2, 4), we need to find the slope of that line and use the point-slope form of the equation. The equation of the line is y = (9/8)x + 25/4.
Step-by-step explanation:
To determine the equation of a line that is parallel to the line joining points A(-5, -1) and B(3, 8), we need to find the slope of that line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Using the given points A(-5, -1) and B(3, 8), the slope of the line is:
slope (m) = (8 - (-1)) / (3 - (-5))
slope (m) = 9 / 8
Since the line we are looking for is parallel, it will have the same slope. Therefore, the slope of the new line is also 9 / 8.
Now, we can use the point-slope form of the equation of a line, which is given by:
y - y1 = m(x - x1)
Using the point C(-2, 4) and the slope 9 / 8, we can substitute these values into the equation and simplify to slope-intercept form:
y - 4 = (9 / 8)(x - (-2))
y - 4 = (9 / 8)(x + 2)
y - 4 = (9 / 8)x + 9 / 4
y = (9 / 8)x + 9 / 4 + 4
y = (9 / 8)x + 25 / 4
Therefore, the equation of the line, in slope-intercept form, that is parallel to the line AB and passing through C, is y = (9 / 8)x + 25 / 4.