Answer:
Parallel slope: -2/3.
Perpendicular slope: 3/2.
Explanation:
To find the equation of the line passing through the given points (1, 3) and (-2, 5), we need to calculate the slope of the line first.
Slope (m) = (change in y) / (change in x)
Slope = (5 - 3) / (-2 - 1) = 2 / -3
Now that we have the slope, use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (1, 3):
y - 3 = (2 / -3)(x - 1)
Simplify this equation:
y - 3 = (-2/3)x + 2/3
To put the equation in slope-intercept form (y = mx + b), we can add 3 to both sides:
y = (-2/3)x + 2/3 + 3
y = (-2/3)x + 11/3
The equation of the line passing through the points (1, 3) and (-2, 5) is
y = (-2/3)x + 11/3.
Calculate the slopes for lines that are parallel and perpendicular to this line.
Parallel slope: The slope of a line parallel to this one will be the same, which is -2/3.
Perpendicular slope: The slope of a line perpendicular to this one will be the negative reciprocal of the slope. Therefore, the perpendicular slope is 3/2.