Question

Which equation represents a line that passes through the two points in the
table?

Answer 1

The equation that represents the line that passes through the given points is y - 1 =
`(5)/(3)` (x - 3) ⇒ A

Explanation:

The point-slope form of the linear equation is y - y1 = m(x - x1), where

• m is the slope of the line

• (x1, y1) is a point on the line

The rule of the slope is m =
`(y2-y1)/(x2-x1)` , where

• (x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (3, 1) and (6, 6)

∴ x1 = 3 and y1 = 1

∴ x2 = 6 and y2 = 6

→ Substitute them in the rule of the slope to find it

∵ m =
`(6-1)/(6-3)=(5)/(3)`

∴ m =
`(5)/(3)`

→ Substitute the value of x1, y1, and m in the form of the equation above

∵ y - 1 =
`(5)/(3)` (x - 3)

∴ The equation that represents the line that passes through the given

points is y - 1 =
`(5)/(3)` (x - 3)