Question

Write the equation of a line that passes through the points shown in the table. Which equations represent a line that passes through the points given in the table? Check all that apply. y – 2 = –6(x + 10) y – 2 = –(x + 10) y – 1 = –(x + 4) y = –6x – 58 y = –x + y = –x + 5

Answer 1

The equations that represent the points on the table are:

$y - 2= -\frac 16 (x +10)$

$y - 1= -\frac 16 (x +4)$

$y - 1= -\frac x6 -\frac 23$

From the table (see attachment, we have):

$(x_1,y_1) = (-10,2)$

$(x_2,y_2) = (-4,1)$

Calculate the slope (m)

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

So, we have:

$m = \frac{1-2}{-4--10}$

$m = \frac{-1}{6}$

$m = -\frac{1}{6}$

The equation is then calculated as follows:

$y = m(x - x_1) + y_2$

This gives:

$y = -\frac 16 (x - -10) + 2$

$y = -\frac 16 (x +10) + 2$

Subtract 2 from both sides

$y - 2= -\frac 16 (x +10)$ ----- option (B)

Add 1 to both sides

$y - 2 + 1= -\frac 16 (x +10) +1$

$y - 1= -\frac 16 (x +10) +1$

Take LCM

$y - 1= -\frac 16 (x +10-6)$

$y - 1= -\frac 16 (x +4)$ ---- option (C)

Open bracket

$y - 1= -\frac x6 -\frac 46$

$y - 1= -\frac x6 -\frac 23$ --- option (E)

Hence, the true options are B, C and E

Read more about linear graphs at:

https://brainly.com/question/20106471