Question

1. what is the equation of the line below? (with a coordinate grid image showing a line)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 3)\) (the y - intercept) and \((-3, 0)\) (when \(y = 0\), we can find the x - intercept by looking at the grid). We can also use another pair of points, for example, \((-2, 1)\) and \((0, 3)\) to calculate the slope.

Step2: Calculate the slope (\(m\))

The formula for the 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's use the points \((-2, 1)\) and \((0, 3)\). Then \(x_1=-2,y_1 = 1,x_2 = 0,y_2=3\).
\(m=\frac{3 - 1}{0-(-2)}=\frac{2}{2}=1\)

Step3: Use the slope - intercept form of a line

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 the line crosses the y - axis at \((0, 3)\), so \(b = 3\) and we found that \(m = 1\).
Substituting \(m = 1\) and \(b = 3\) into the equation \(y=mx + b\), we get \(y=x + 3\)

Answer:

\(y=x + 3\)