Question

Select the equation that represents a line with a slope of 3 and that contains the point (-4,2).

A) y - 2 = 3(x+4)

B) y+2=3(x-4)

C) x-4=3(y+4)

D)x-4=3(y+2)

Answer 1

A is correct option. Equation of line: y-2=3(x+4)

Explanation:

Slope of line is 3 and passing point (-4,2).

If slope and passing point given then we have an equation of line

`y-y_1=m(x-x_1)`

where,

`(x_1,y_1)\rightarrow (-4,2)`

Slope (m)=3

Equation of line:

y-2=3(x+4)

This equation match with option A

Thus. option A is correct.

Answer 2

A) y - 2 = 3(x+4)

Explanation:

Given that the equation is a line with slope =m=3 and

a point on it (x1,y1) = (-4,2)

Any line having slope m and passing through (x1,y1) has equation in point slope form as

y-y1 = m(x-x1)

We are given here x1 =-4, y1 =2 and m =3

y-y1 = y-2 and x-x1 = x-(-4) = x+4

So equation is y-2 = 3(x+4)

Verify:

The line is y = 3x+12+2 = 3x+14

Hence slope =3 is verified

Substitute the point x =-4 and y =2

2 =3(-4)+14 = 2 is true

Thus verified