Question

Line l contains the points (3,1) and (4,4). If line m is a different line, parallel to line l in the same coordinate plane, which of the following could be the equation of line m?

a. y = 3x - 8
b. y = 1/3x - 3
c. y = -3x - 8
d. y = 3x + 1
e. y = -8x + 3

Answer 1

First you need to fine the slope
3,1
4,4
The slope with be m= 3
then put it in point slope from
y-1=3(x-3)
y-1=3x-9
y=3x-8

so the answer with be "A"

Answer 2

Option D is the correct answer.

Explanation:

Slopes of parallel lines are same. Here l and m are parallel, so their slopes must be equal.

Given two points of line l, so we can calculate slope of l.

Points are (3,1) and (4,4),

`m_l=(y_2-y_1)/(x_2-x_1)=(4-1)/(4-3)=3`

Equation of line l,

y - y₁ = m(x-x₁)

y - 1 = 3( x -3)

y = 3x - 8

Slope of line line l = Slope of line line m = 3

The options are given in the form, y = mx + c

Slope of option A = 3 ( But it is the equation of line l)

Slope of option B = 1/3

Slope of option C = -3

Slope of option D = 3 ( slope is same)

Slope of option E = -8

So we can see option D is the correct answer.