Question

Find the equation of the line passing through (−2,3). Use symbolic notation and fractions where needed.) 1. Parallel to the line y=4x−5:y= 2. Perpendicular to the line y=3x−5:y=

Answer 1

The equation of the line parallel to y = 4x - 5 passing through (-2, 3) is y = 4x + b, and to find the value of b, we substitute the coordinates (-2, 3) into the equation and solve for b. The equation of the line perpendicular to y = 3x - 5 passing through (-2, 3) is y - 3 = -1/3(x - (-2)).

Step-by-step explanation:

To find the equation of a line parallel or perpendicular to a given line, we need to know the slope of the given line. For the line y = 4x - 5, the slope is 4, so any line parallel to it will have the same slope. Therefore, the equation of the line parallel to y = 4x - 5 passing through (-2, 3) is y = 4x + b. To find the value of b, we substitute the coordinates (-2, 3) into the equation and solve for b. For the line perpendicular to y = 3x - 5, the slope is the negative reciprocal of 3, which is -1/3. Using the point-slope form, the equation of the line perpendicular to y = 3x - 5 passing through (-2, 3) is y - 3 = -1/3(x - (-2)).

Learn more about Equation of Lines