Question

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line. the only cordinates are (3,-2)​

Answer 1

The equation of a line parallel to y = 9 + 3x that passes through (3, -2) is y = 3x - 11, and the equation of a line perpendicular to y = 9 + 3x that passes through (3, -2) is y = -1/3x + 1.

Step-by-step explanation:

The equation of a line that is parallel to the line y = 9 + 3x will have the same slope, which is 3.

To find the y-intercept of our parallel line, we use the point (3, -2) and the slope 3 in the point-slope form which is y - y1 = m(x - x1).

Substituting the given point and slope, we get y + 2 = 3(x - 3), which simplifies to y = 3x - 11.

To find the equation of a line perpendicular to y = 9 + 3x, we need a slope that is the negative reciprocal of 3, which is -1/3.

Using the point (3, -2) and the slope -1/3 in the point-slope formula, we get y + 2 = -1/3(x - 3), which simplifies to y = -1/3x + 1.