Question

Which is not an equation of the line going through (3, -6) and (1, 2)?

O A. y+ 6= -4(x-3)
O B. y-1=-4(x-2)
O C. y=-4x+6
O D. y - 2 = -4(x - 1)

Answer 1

B, C

Explanation:

The equation of a line can be given by y -y₁= m(x -x₁), where m is the slope. This is also known as the point-slope form.

`\boxed{ slope = (y _(1) - y_2 )/(x_1 - x_2) }`

Slope of the line

`= (2 - ( - 6))/(1 - 3)`

`= (2 + 6)/( - 2)`

`= (8)/( - 2)`

= -4

Substitute m= -4 into the equation:

y -y₁= -4(x -x₁)

Substitute a pair of coordinates into (x₁, y₁):

Let's start by substituting (1, 2).

y -2= -4(x -1)

This gives us the same equation as D, making D an incorrect option. Note that the question asks for which is not the correct equation.

Let's change the above into the slope-intercept form, where by y is the subject of formula.

Start by expanding the right-hand side:

y -2= -4x +1

+2 on both sides:

y= -4x +3

This equation is not the same as C. C is thus the correct option.

Let's check for options A and B.

The equation in option B is not the correct equation either as they have substituted (2, 1) instead of (1, 2) into (x₁, y₁). Thus, option B is also correct.

y -y₁= -4(x -x₁)

Substitute (3, -6) into (x₁, y₁):

y -(-6)= -4(x -3)

y +6= -4(x -3)

This is the same as option A, making option A incorrect too.