Question

Select the equation which represents the graph.

Question 1 options:

A: y − 3 = 3/2(x − 4)

B: y − 3 = 2/3(x − 4)

C: y − 3 =− 2/3(x − 4)

D: y − 3 = −3/2(x − 4)

Answer 1

B.
`y - 3 = (2)/(3)(x - 4)`

Explanation:

We can create an equation to represent the graph in point-slope form, given as
`y - y_1 = m(x - x_1)`, by using a point (x1, y1) on the line, (4, 3) and the slope (m) of the line.

Let's find slope using the two points (4, 3) and (-2, -1).

`slope (m) = (y_2 - y_1)/(x_2 -x_1) = (-1 - 3)/(-2 - 4) = (-4)/(-6) = (2)/(3)`

Substitute m = ⅔, x1 = 4, and y1 = 3 in
`y - y_1 = m(x - x_1)`.

The equation that represents the graph would be:

✅
`y - 3 = (2)/(3)(x - 4)`,