Question

which function is best represented by this graph?
a ( y = 3x + 2 )
b ( y = -2x + 3 )
c ( y = 2x - 1.5 )
(graph of a line on a coordinate plane with grid lines)

Explanation:

Step1: Find the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the graph, when \(x=0\), \(y = 2\). The equation of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Calculate the slope \(m\)

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line, say \((0,2)\) and \((2, - 2)\). Then \(m=\frac{-2 - 2}{2-0}=\frac{-4}{2}=-2\)

Step3: Write the equation of the line

Using the slope - intercept form \(y = mx + b\), with \(m=-2\) and \(b = 2\), the equation is \(y=-2x + 2\) (but wait, let's check another way. Wait, no, let's check the options.
Another way: check the slope from the graph. The line is decreasing (going down from left to right), so the slope \(m<0\).
For option A: \(y = 3x+2\), slope \(m = 3>0\) (rejected).
For option B: \(y=-2x + 3\), slope \(m=-2\). If \(x = 0\), \(y=3\) (rejected as y - intercept from graph is \(y = 2\)).
For option C: \(y=2x-1.5\), slope \(m = 2>0\) (rejected).
For option D: assume there was a typo (maybe the intended equation is \(y=-2x + 2\) which is not listed. But if we check the general form. Wait, wait, re - check the slope calculation.
Take two points \((0,2)\) and \((1,0)\) (approximate from the graph). Then \(m=\frac{0 - 2}{1-0}=-2\). If we assume the options, maybe there was a mis - label. But if we go by the slope (negative) and y - intercept (around \(y = 2\) in the options, the closest is if we consider the general process of elimination.
Wait, no, re - check:
The slope formula \(m=\frac{y_2-y_1}{x_2 - x_1}\). Let’s take two clear points. Suppose the line passes through \((0,2)\) (y - intercept) and \((1,0)\)
\(m=\frac{0 - 2}{1-0}=-2\).
The equation \(y=-2x+2\) is not in the options. But if we check the options again:
Option B: \(y=-2x + 3\). If \(x = 0\), \(y = 3\) (not \(2\)). But if we consider that maybe the graph was mis - drawn (in a test - taking situation, if we assume the options and the slope (negative) is the key. Since options A and C have positive slopes (lines increasing), and option B has slope \(m=-2\) (line decreasing)

Answer:

B. \(y=-2x + 3\)