Question

1. what is the equation of the line below?

Explanation:

Step1: Identify two points on the line

Looking at the graph, let's assume the two red points have coordinates. Let's say the lower point is \((-6, -5)\) and the upper point is \((-3, -2)\) (we can check the grid to confirm the coordinates by counting the units from the origin).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the two points \((x_1,y_1)=(-6, -5)\) and \((x_2,y_2)=(-3, -2)\):

$$ m=\frac{-2 - (-5)}{-3 - (-6)}=\frac{-2 + 5}{-3 + 6}=\frac{3}{3}=1 $$

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 \((-3, -2)\) and \(m = 1\):

$$ y-(-2)=1\times(x - (-3)) $$

Simplify the equation:

$$ y + 2=x + 3 $$

Subtract 2 from both sides:

$$ y=x + 1 $$

We can verify with the other point. If \(x=-6\), then \(y=-6 + 1=-5\), which matches the \(y\) - coordinate of the lower point.

Answer:

The equation of the line is \(y = x+1\)