Question

What is an equation of the line with slope 3 that goes through point (2/3,4)?

A.y=3x+2
B.y=3x+4
C.y=3x+6
D.y=3x-6

Answer 1

A. y = 3x + 2

Explanation:

`\left((2)/(3);\ 4\right)\to x=(2)/(3),\ y=4\\\\\text{Put to the each equation:}\\\\A.\ y=3x+2\\\\4=3\left((2)/(3)\right)+2\\4=2+2\\4=4\qquad\bold{CORRECT}`

We do not check other equations because all the lines have the same slope. Therefore, they are parallel lines. If one of the lines passes through a given point, then another cannot pass through that point.

Answer 2

A

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3, thus

y = 3x + c ← is the partial equation of the line

To find c substitute (
`(2)/(3)`, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = 3x + 2 → A