Question

Which equations represent the data in the table? Check all that apply.

Answer 1

Answer

y - 3.5 = -1.25x

Step by step explanation

y - 6 = x + 2 is fails at x = 0

y -2 = -(x - 1) is fails at x = -2

y + 2 = (x - 6) is fails at x = 0

y -1 = -(x - 2) is fails at x = 0

y - 3.5 = -1.25x is true for all values of x.

Answer is y - 3.5 = -1.25x

Thank you.

Answer 2

ANSWER

The correct answer is
$y - 3.5 = - 1.25x$

EXPLANATION

One of the best ways to approach this question is to find the equation of the line that represent the values in the table.

So we need the slope. We can find the slope using any two pairs of points say
$(-2,6) \: and \: (0,3.5)$

The slope is given by the formula,
$m = \frac{ y_2-y_1}{ x_2-x_1}$

This implies that,

$m = \frac{6 - 3.5}{ - 2 - 0}$
$m = - \frac{2.5}{2} = - 1.25$

We see from the table that the y-intercept is
$(0,3.5).$

Hence the equation is

$y = mx + c$

where m=-1.25 is the slope and c=3.5 is the y-intercept.

We substitute to obtain,

$y = - 1.25x + 3 .5$

or

$y - 3.5 = - 1.25x$

This is the only equation that represents the values in the table.

The answer is D.