Question

Line L passes through (3,5) and is parallel to y = 6x-2. Find the equation of line L

Answer 1

The equation of line L, which is parallel to y = 6x - 2 and passes through the point (3,5), is y = 6x - 13.

Step-by-step explanation:

Since line L is parallel to the given line y = 6x - 2, they must have the same slope. The given line has a slope of 6, which we can see from the coefficient of x in its equation. To find the equation of line L that passes through the point (3,5), we use the point-slope formula:

y - y1 = m(x - x1), where (x1,y1) is the point the line passes through and m is the slope.

Plugging in our values, we get:

y - 5 = 6(x - 3)

Simplifying:

y - 5 = 6x - 18

y = 6x - 13

Therefore, the equation of line L is y = 6x - 13.

Answer 2

y = 6m - 13

Step-by-step explanation:

Parallel lines have the same slope. The slope in the equation y = 6x -2 is 6.

To write an equation in the slope intercept form, we need a slope and a y-intercept. We have the slope, we need to find the y-intercept.

To find the y intercept, we need a slope, and x on the line and a y on the line. The point (3,5) gives us the x and the y.

slope = 6

x = 3

y = 5

y = mx + b plug in what we know and solve for b

5 = 6(3) + b

5 = 18 + b Subtract 18 from both sides of the equation

-13 = b

y = mx + b

y = 6m - 13