Question

question 1 pts
which is the graph of the line ( y - 2 = 3(x - 1) )?
(options with graphs: a, b, c, d)
question 1 pts
which equation represents the graphed line?
a ( y - 1 = -2(x - 3) )
b ( y - 1 = -2(x + 3) )
c ( y + 1 = -2(x - 3) )
d ( y + 1 = -2(x + 3) )
(graph provided for this question)

Explanation:

Step1: Analyze the first line equation

The equation is $y - 2 = 3(x - 1)$. Convert to slope-intercept form: $y = 3x - 3 + 2 = 3x - 1$. The slope is 3 and the y-intercept is -1. Check the graphs: option B has a slope of 3 and passes through (0, -1), so it matches.

Step2: Analyze the second graph

The graphed line has a slope of -2 (since it goes down 2 units for every 1 unit right). It passes through (3, -1). Using point-slope form $y - y_1 = m(x - x_1)$, substitute $m=-2$, $x_1=3$, $y_1=-1$: $y - (-1) = -2(x - 3)$ which simplifies to $y + 1 = -2(x - 3)$, so option C matches.

Answer:

B, C