Question

Write an equation for the line parallel to the given line that contains C.

C(3,4); y=6/7x-8

Answer 1

To write the equation of a line parallel to y=6/7x-8 and passing through C(3,4), we use the same slope of 6/7 and the point (3,4) to get y - 4 = 6/7(x - 3). In slope-intercept form, the equation is y = 6/7x + 10/7.

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through point C(3,4), we first need to determine the slope of the parallel line. Parallel lines have the same slope, so the slope of the new line will be the same as the slope of the given line, which is 6/7.

Next, we use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Since our line must go through point C(3,4) and has a slope of 6/7, the equation becomes:

y - 4 = 6/7(x - 3).

To put it in slope-intercept form, distribute the slope on the right-hand side and then solve for y to get:

y = 6/7x - 6/7(3) + 4

After distributing and combining like terms, the final equation of our line is:

y = 6/7x + 10/7

Answer 2

Remember the equation of a line: y=mx + b where m is the slope and b is the vertical offset of the line.

So a line parallel to the equation will have the same slope (m) but a different (b).

The new equation will be y=6/7x + b.

To find b, plug in (3,4) x=3 and y=4 to find the new b since (3,4) is on the new line.

Solve 4=6/7*3 + b

b = 4 - 6/7*3