Question

Write an equation of a line passing through the point (-1, 3) and parallel to AB with A(3, -5) and B(-2, 15)

Answer 1

To find the equation of a line parallel to AB with A(3, -5) and B(-2, 15), you need to determine the slope of line AB and then use the point-slope form to write the equation. The equation of the line parallel to AB passing through (-1, 3) is y = -4x - 1.

Step-by-step explanation:

To find the equation of a line parallel to AB with A(3, -5) and B(-2, 15), you need to determine the slope of line AB. The slope of a line can be found using the formula: slope = (y2 - y1) / (x2 - x1). In this case, the slope of line AB is (15 - (-5)) / (-2 - 3) = 20 / -5 = -4. Since the parallel line will have the same slope, the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept. Given that the line passes through the point (-1, 3), we can substitute these values into the equation to find the value of b. We have 3 = -4(-1) + b, which simplifies to 3 = 4 + b. Rearranging, we find b = -1. Therefore, the equation of the line parallel to AB passing through (-1, 3) is y = -4x - 1.

Answer 2

Step-by-step explanation:

Line AB has a Slope of -20/5 or -4. Since the line that is being calculated is parallel it has the same slope. We can plug this Slope and the given point of the line into the point Slope equation for an equation of y - 3 = -4 (x + 1).