Question

1. a coordinate grid with a line plotted. the line passes through various grid points, with axes labeled x and y, and grid lines visible. the x-axis ranges from -8 to 8, and the y-axis ranges from -8 to 8.

Explanation:

Step1: Identify two points

From the graph, we can see that the line passes through \((0, 4)\) (the y - intercept) and \((4, 0)\) (the x - intercept). We can also use another point like \((- 4,8)\) (from the left side of the graph). Let's use \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(4,0)\) to find the slope.
The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Substitute the values: \(m=\frac{0 - 4}{4-0}=\frac{-4}{4}=- 1\)

Step2: Use slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=-1\) and from the point \((0,4)\), the y - intercept \(b = 4\). So the equation of the line is \(y=-x + 4\)

(If the problem was to find the equation of the line, this is the process. If it was something else like finding the slope, we already found \(m=-1\) in Step 1)

Answer:

If the question was to find the equation of the line, the answer is \(y=-x + 4\); if it was to find the slope, the answer is \(-1\)