Question

Both lines have a slope of (3)/(2). One passes through the point (-1,-3), and the other passes through the point (3,1)

Answer 1

To find the equations of the lines with a slope of 3/2 passing through different points, we can use the point-slope form of the equation of a line.

Step-by-step explanation:

To find the equation of a line given its slope and a point it passes through, we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

1. For the line passing through (-1,-3) with a slope of 3/2, we substitute x1=-1, y1=-3, and m=3/2 into the point-slope equation to get y - (-3) = (3/2)(x - (-1)).
2. Simplifying this equation gives us y + 3 = (3/2)(x + 1).
3. For the line passing through (3,1) with the same slope of 3/2, we substitute x1=3, y1=1, and m=3/2 into the point-slope equation to get y - 1 = (3/2)(x - 3).
4. Simplifying this equation gives us y - 1 = (3/2)x - (9/2).

Therefore, the equations of the lines are y + 3 = (3/2)(x + 1) and y - 1 = (3/2)x - (9/2).