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

The red point is at \((4, -7)\) (wait, no, looking at the graph, the red point seems to be at \((4, -7)\)? Wait, no, let's check the grid. Wait, the x-axis: from 0 to 4, and y-axis: the red point is at x=4, y=-7? Wait, no, maybe I misread. Wait, the line crosses the x-axis at (5, 0)? Wait, no, the grid: each square is 1 unit. Let's find two points. Let's take the red point: let's see, the red point is at (4, -7)? Wait, no, maybe (4, -7) and another point. Wait, when x=5, y=0? Wait, no, let's calculate the slope. Wait, let's find two points on the line. Let's take (5, 0) and (4, -7)? No, that can't be. Wait, maybe the red point is (4, -7) and another point is (5, 0)? Wait, no, the slope between (4, -7) and (5, 0) is \(\frac{0 - (-7)}{5 - 4} = 7\). Wait, that makes sense. Wait, let's check: from (4, -7) to (5, 0), the change in y is 7, change in x is 1, so slope \(m = 7\).

Step2: Recall point - slope form

The point - slope form of a line is \(y - y_1 = m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope.

We have the red point \((x_1,y_1)=(4, - 7)\) and slope \(m = 7\).

Substitute into the point - slope formula: \(y - (-7)=7(x - 4)\), which simplifies to \(y + 7 = 7(x - 4)\).

Wait, let's verify the slope again. Let's take two points: when x = 4, y=-7; when x = 5, y = 0. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0-(-7)}{5 - 4}=\frac{7}{1}=7\). So the slope is 7. The red point is (4, -7). So using point - slope form with \((x_1,y_1)=(4, - 7)\) and \(m = 7\), we get \(y - (-7)=7(x - 4)\), i.e., \(y + 7 = 7(x - 4)\).

Answer:

\(y + 7 = 7(x - 4)\)