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

Answer:

x + 2y = 2

Step-by-step explanation:

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

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

Substitute:

$m=\dfrac{0-4}{2-(-6)}=\dfrac{-4}{8}=-\dfrac{1}{2}$

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

$0=-\dfrac{1}{2}(2)+b$

$0=-1+b$          add 1 to both sides

$1=b\to b=1$

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

$y=-\dfrac{1}{2}x+1$

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

$y=-\dfrac{1}{2}x+1$           multiply both sides by 2

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

$x+2y=2$

Answer 2

Answer:

Option 1.

Step-by-step 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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

Using the above formula the equation of line is

$y-(4)=\dfrac{0-4}{2-(-6)}(x-(-6))$

$y-4=\dfrac{-4}{8}(x+6)$

$y-4=\dfrac{-1}{2}(x+6)$

Muliply both sides by 2.

$2y-8=-x-6$

$x+2y=-6+8$

$x+2y=2$

Therefore, the correct option is 1.