Question

look at this graph: what is the equation of the line in point - slope form? use the red point in your equation. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify the red point and another point

From the graph, the red point seems to be at \((20, -100)\) (assuming the grid and the position; also, the y-intercept is at \((0, 20)\)? Wait, no, looking again: when \(x = 0\), the line crosses the y-axis at \(y = 20\)? Wait, no, the line goes from top left to bottom right. Wait, let's check the slope. Let's take two points: let's say the y-intercept is \((0, 20)\) and the red point is \((20, -100)\)? Wait, no, maybe the red point is \((20, -100)\) and another point, say when \(x = 0\), \(y = 20\)? Wait, no, the line passes through \((0, 20)\) and \((20, -100)\)? Wait, no, let's calculate the slope. Slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: let's see, when \(x = 0\), \(y = 20\) (wait, no, the line is going down, so maybe when \(x = 0\), \(y = 20\) and when \(x = 20\), \(y = -100\)? Wait, no, the red point is at (20, -100)? Wait, the grid: each square is 10? Wait, the x-axis: from 0 to 20 is two squares? Wait, maybe the red point is at \((20, -100)\) and the y-intercept is \((0, 20)\)? Wait, no, let's check the slope. Let's take \((0, 20)\) and \((20, -100)\). Then \(m=\frac{-100 - 20}{20 - 0}=\frac{-120}{20}=-6\). Wait, but maybe the red point is \((20, -100)\)? Wait, the problem says to use the red point. Let's confirm the red point's coordinates. Looking at the graph, the red point is at \(x = 20\), \(y = -100\) (since it's at the bottom right, 20 on x, -100 on y). And another point: when \(x = 0\), the line crosses the y-axis at \(y = 20\)? Wait, no, the line is going from (0, 20) to (20, -100)? Wait, no, maybe the y-intercept is (0, 20)? Wait, no, the line is steeply decreasing. Wait, let's recalculate. Let's take two points: let's say (0, 20) and (20, -100). Then the slope \(m=\frac{-100 - 20}{20 - 0}=\frac{-120}{20}=-6\). So the slope is -6. The red point is (20, -100).

Step2: Write point - slope form

Point - slope form is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is the red point \((20, - 100)\) and \(m=-6\). So substituting, we get \(y - (-100)=-6(x - 20)\), which simplifies to \(y + 100=-6(x - 20)\).

Answer:

\(y + 100=-6(x - 20)\)