Question

Find a​ point-slope equation of the line having the given slope and containing the given point.
m = 4/5​, ​(4​,6​)

Answer 1

The point-slope equation of a line is given by the formula:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

In this case, the slope is 4/5 and the point on the line is (4, 6).

Substituting these values into the formula, we get:

y - 6 = (4/5)(x - 4)

Simplifying this equation, we multiply the slope 4/5 by (x - 4):

y - 6 = 4/5 * x - 4 * 4/5

y - 6 = 4/5 * x - 16/5

Combining like terms, we get:

y = 4/5 * x - 16/5 + 6

y = 4/5 * x - 16/5 + 30/5

y = 4/5 * x + 14/5

So, the point-slope equation of the line with a slope of 4/5 and passing through the point (4, 6) is y = 4/5 * x + 14/5.