Question

A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?

y=-x+1
y=1/√x+7
y=-2x-8
y = 2x + 16

Answer 1

y=
`-(1)/(2)x`+1

Explanation:

y = mx plus c,where m is the gradient.

∴m =
`(y2-y1)/(x2-x1)`=
`(2-4)/(-2-(-6))`=
`(-2)/(4)`=
`-(1)/(2)`

Equation of a line equals

y-y1=m(x-x1) (Using point (-6, 4) for x1 and y1 values)

y-4=
`-(1)/(2)`(x-(-6))

y-4=
`-(1)/(2)`(x+6)

y-4=
`-(1)/(2)`x-3

2(y-4)=-x-3(2)(multiply through by 2)

2y-8=-x-6

2y=-x+2(divide through by 2)

y=
`-(1)/(2)x`+1

∴the equation of the line is y=
`-(1)/(2)x`+1

Answer 2

Correct answer not shown on the options.

y = -(1/2)+1

Explanation:

Let's find an equation in the format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

The slope can be calculated as the Rise/Run of the line between the two given points (-6,4) and (-2,2):

Rise = (2 - 4) = -2

Run = (-2 - (-6)) = 4

Slope = Rise/Run = -2/4 or -(1/2)

In fact, the actual full equation is y= -(1/2)x+1 (See attached graph).

None of the options have a slope of -(1/2). Either the information on the two points or the options are incorrect.