Question

1. graph of a line on a coordinate grid with x-axis from -8 to 8 and y-axis from -8 to 8

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -4)\) (the y - intercept) and \((1, -7)\) (by observing the grid, when \(x = 1\), \(y=-7\)).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 4)\) and \((x_2,y_2)=(1, - 7)\). Then \(m=\frac{-7-(-4)}{1 - 0}=\frac{-7 + 4}{1}=\frac{-3}{1}=-3\).

Step3: Use slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know \(m=-3\) and \(b=-4\) (from the point \((0,-4)\)). So the equation of the line is \(y=-3x-4\).

(Assuming the problem is to find the equation of the line. If the problem was different, for example, finding the x - intercept: set \(y = 0\) in \(y=-3x - 4\), then \(0=-3x-4\), \(3x=-4\), \(x =-\frac{4}{3}\approx - 1.33\), which matches the graph as the line crosses the x - axis between \(x=-2\) and \(x = 0\).)

Answer:

If the question is to find the equation of the line, the answer is \(y=-3x - 4\). If the question is to find the slope, the answer is \(-3\). If the question is to find the y - intercept, the answer is \(-4\). (Since the original problem was not fully stated, but based on the graph of a line, these are common calculations. Assuming the most common task is finding the equation, the answer is \(y=-3x - 4\))