Question

Choose the equation that represents a line that passes through points (−6, 4) and (2, 0). x + 2y = 2 2x − y = −16 x + 2y = −8 2x + y = 4

Answer 1

Option 1.

Explanation:

It is given that the line passes through the points (-6,4) and (2,0).

If a line passes through two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Using the above formula the equation of line is

`y-(4)=(0-4)/(2-(-6))(x-(-6))`

`y-4=(-4)/(8)(x+6)`

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

Muliply both sides by 2.

`2y-8=-x-6`

`x+2y=-6+8`

`x+2y=2`

Therefore, the correct option is 1.

Answer 2

x + 2y = 2

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

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We have the points (-6, 4) and (2, 0).

Substitute:

`m=(0-4)/(2-(-6))=(-4)/(8)=-(1)/(2)`

Put the value of the slope and coordinates of the point (2, 0) to the equation of a line:

`0=-(1)/(2)(2)+b`

`0=-1+b` add 1 to both sides

`1=b\to b=1`

The equation of a line in the slope-intercept form:

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

Convert to the standard form
`Ax+By=C`

`y=-(1)/(2)x+1` multiply both sides by 2

`2y=-x+2` add x to both sides

`x+2y=2`