Question

Find the equation of the lines passing through (-3,5) and having the following characteristics. Leave your answer in point slope form. Slope of 7/16, parallel to the line 5x - 3y = 3, passing through the origin, parallel to the y-axis.

A. (y = 7/16(x + 3))
B. (y = 7/16(x - 3))
C. (y = 16/7(x + 3))
D. (y = 16/7(x - 3))

Answer 1

To find the equation of lines passing through a given point, we use the point-slope form. The equations are: a) y = (5/3)x + 7, b) y = (7/16)x, c) x = 0.

Step-by-step explanation:

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

a) Since the line is parallel to the line 5x - 3y = 3, it will have the same slope. The slope of the line 5x - 3y = 3 can be found by rearranging the equation to y = (5/3)x - 1. So, the slope is 5/3. Now, using the point (-3,5), the equation of the line is: y - 5 = (5/3)(x - (-3)). Simplifying gives y = (5/3)x + 7.

b) For a line passing through the origin with a slope of 7/16, we use the point (0,0) and the slope to get the equation: y - 0 = (7/16)(x - 0). Simplifying gives y = (7/16)x.

c) Since the line is parallel to the y-axis, the slope is undefined. The equation will have the form x = k, where k is the x-coordinate of any point on the line. Since the line passes through the origin, the equation is simply x = 0.