Question

1. what is the equation of the line below?

Explanation:

Step1: Identify two points on the line

Looking at the graph, the two red dots (points) on the line seem to be at \((2, -1)\) and \((4, 3)\) (assuming each grid square is 1 unit). Let's confirm the coordinates: from the origin, moving 2 units right (x = 2) and 1 unit down (y = -1) for the lower point, and 4 units right (x = 4) and 3 units up (y = 3) for the upper point.

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((x_1,y_1)=(2, -1)\) and \((x_2,y_2)=(4, 3)\), we substitute:
\(m=\frac{3 - (-1)}{4 - 2}=\frac{3 + 1}{2}=\frac{4}{2}=2\)

Step3: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Let's use the point \((2, -1)\) and \(m = 2\).
Substitute into the formula: \(y-(-1)=2(x - 2)\)
Simplify: \(y + 1=2x-4\)
Subtract 1 from both sides: \(y=2x-4 - 1\), so \(y = 2x-5\)

Answer:

The equation of the line is \(y = 2x-5\)