How to write a linear equation from a data table

Asked by admin @ 29/10/2021 in Mathematics viewed by 308 People

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

y – 6 = (x + 2)
y – 2 = –(x – 1)
y + 2 = (x – 6)
y – 1 = –(x – 2)
y – 3.5 = –1.25x

Answered by admin @ 29/10/2021

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.

How to write a linear equation from a data table

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