Question

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

The red point is at \((60, 10)\) (assuming each grid square is 10 units? Wait, no, looking at the grid: the x-axis at 60, y-axis: let's check the grid. Wait, the red point: x=60, y=10? Wait no, maybe each grid is 10? Wait the line: let's find two points. Let's see, when x=60, y=10? Wait no, maybe another point. Wait, the line is steep. Let's take two points. Let's say when x=60, y=10 (red point), and when x=50, y=10 - slope(10)? Wait no, maybe the slope is calculated by rise over run. Let's see, the line goes from (60,10) to (50, 10 - m10). Wait, maybe the slope is 10? Wait, no, let's check the grid. Wait, the vertical axis: from -100 to 40, each grid is 10. Horizontal: from -100 to 100, each grid is 10. So the red point is at (60, 10)? Wait, no, looking at the graph, the red point is on the line, at x=60, y=10? Wait, no, maybe the slope is 10. Wait, let's take two points: (60,10) and (50, 10 - 101) = (50, 0)? No, that doesn't make sense. Wait, maybe the slope is 10. Wait, let's calculate slope. Let's take two points: (60,10) and (50, 10 - 1010)? No, that's not right. Wait, maybe the line passes through (60,10) and (50, 10 - 1010)? No, that's too steep. Wait, maybe the slope is 10. Wait, point-slope form is \( y - y_1 = m(x - x_1) \), where \((x_1, y_1)\) is the red point. Let's find the slope. Let's see, when x increases by 10, y increases by 100? Wait, no, the line goes from (60,10) to (50, 10 - 100) = (50, -90)? Wait, that's a difference of x: -10, y: -100. So slope \( m = \frac{-100}{-10} = 10 \). Yes, that makes sense. So slope m=10. The red point is (60,10). So point-slope form is \( y - 10 = 10(x - 60) \). Wait, let's check: when x=60, y=10, which matches. When x=50, y=10 + 10(-10) = 10 - 100 = -90, which is on the line (since at x=50, y=-90, which is a grid point). So that works.

Step2: Write point-slope form

Using the red point \((60, 10)\) and slope \( m = 10 \), the point-slope form is \( y - 10 = 10(x - 60) \). Wait, but let's confirm the slope. Let's take (60,10) and (50, -90). The change in y is -90 - 10 = -100, change in x is 50 - 60 = -10, so slope is \( \frac{-100}{-10} = 10 \). Correct. So the point-slope form is \( y - 10 = 10(x - 60) \).

Answer:

\( y - 10 = 10(x - 60) \)