Question

which of the following equations does the graph below represent? (graph of a line in a coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10, passing through (0,8) and (1, -something) approximately)

Explanation:

Step1: Identify the slope and y-intercept

The graph is a straight line, so it's a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. From the graph, the line crosses the y-axis at \( (0, 8) \), so \( b = 8 \). To find the slope, we can use two points. Let's take \( (0, 8) \) and \( (1, -2) \) (estimating from the graph's steepness). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 8}{1 - 0} = -10 \)? Wait, no, maybe better to check the x-intercept. The line crosses the x-axis at \( (1, 0) \) (approx). So using \( (0, 8) \) and \( (1, 0) \), slope \( m = \frac{0 - 8}{1 - 0} = -8 \). Wait, maybe the equation is \( y = -8x + 8 \)? Wait, no, let's think again. Wait, when x=0, y=8 (y-intercept b=8). When y=0, x=1 (since it crosses x-axis at (1,0)). So slope \( m = \frac{0 - 8}{1 - 0} = -8 \). So the equation is \( y = -8x + 8 \)? Wait, but let's check another point. If x=1, y= -8(1) +8=0, which matches. If x=0, y=8, which matches. So the equation should be \( y = -8x + 8 \). Wait, but maybe the options (not shown here) would have this. Wait, the key steps are: 1. Recognize it's a linear equation (straight line). 2. Find y-intercept (b) from where it crosses y-axis (0,8). 3. Find slope (m) using two points (0,8) and (1,0) or other points. 4. Form the equation \( y = mx + b \).

Step2: Form the equation

Using the y-intercept \( b = 8 \) and slope \( m = -8 \) (from points (0,8) and (1,0)), the equation is \( y = -8x + 8 \).

Answer:

The equation is \( y = -8x + 8 \) (assuming the options include this; if options were given, we'd match, but based on the graph, this is the derived equation).