Question

1. (the chart is a coordinate grid with a line passing through points, and the number 5 is marked at the top left of the chart.)

Explanation:

To determine the equation of the line, we can use the two - point form or the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step 1: Identify two points on the line

From the graph, we can see that the line passes through the points \((- 2,2.5)\) (wait, actually, looking at the grid, let's find two clear points. Let's take the y - intercept first. The line crosses the y - axis at \((0,-3)\) (the point with coordinates \((0, - 3)\)) and another point, say \((-2,2)\) (the point with \(x=-2\) and \(y = 2\)).

Step 2: Calculate the slope (\(m\))

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,-3)\) and \((x_2,y_2)=(-2,2)\). Then \(m=\frac{2-(-3)}{-2 - 0}=\frac{2 + 3}{-2}=\frac{5}{-2}=-\frac{5}{2}\)

Step 3: Determine the y - intercept (\(b\))

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-3)\), we can see that \(b=-3\)

Step 4: Write the equation of the line

Using the slope - intercept form \(y=mx + b\), substitute \(m =-\frac{5}{2}\) and \(b=-3\). So the equation of the line is \(y=-\frac{5}{2}x-3\)

If we want to check with another point, let's take the x - intercept. The x - intercept is when \(y = 0\). So \(0=-\frac{5}{2}x-3\), \(\frac{5}{2}x=-3\), \(x=-\frac{6}{5}=-1.2\), which matches the graph (the line crosses the x - axis at \(x=-1\) approximately, and \(-\frac{6}{5}=-1.2\) is close, considering the grid).

If the question was to find the equation of the line, the answer is \(y =-\frac{5}{2}x-3\)

(If the question was different, for example, finding the slope, the slope is \(-\frac{5}{2}\), or finding the y - intercept, the y - intercept is \(-3\). Since the original problem was not fully stated, but based on the graph, a common question is to find the equation of the line. )

Answer:

The equation of the line is \(y =-\frac{5}{2}x - 3\)