Question

The graphed line can be expressed by which equation?y+2=23(x+2) y−2=34(x−1) y−1=−34(x−2) y−2=34(x−2)

Answer 1

For this case we have that by definition, the equation of a line in the point-slope form is given by:

$y-y_ {0} = m (x-x_ {0})$

Where:

$(x_ {0}, y_ {0}):$It is a point through which the line passes

m: It is the slope of the line

According to the graph we have that the line goes through the following points:

$(x_ {1}, y_ {1}) :( 4,2)\\(x_ {2}, y_ {2}): (- 2, -2)$

We found the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-2} {- 2-4} = \frac {-4} {- 6} = \frac {2} {3}$

We choose a point:

$(x_ {0}, y_ {0}): (-2, -2)$

The equation of the line is:

$y - (- 2) = \frac {2} {3} (x - (- 2))\\y + 2 = \frac {2} {3} (x + 2)$

ANswer:

$y + 2 = \frac {2} {3} (x + 2)$

Option A