Question

what is the equation of the line in point - slope form?

Explanation:

Step1: Identify the point

The red dot is at (60, 15) (assuming the grid has each square as 5 units? Wait, no, looking at the y-axis, from 0 to 20 is 2 units? Wait, no, the y-axis: 0, then -20, -40, etc. Wait, the red dot is at x=60, and let's check the slope. Wait, maybe each grid square is 5? Wait, no, let's see the line. Wait, maybe the slope is calculated as rise over run. Let's find two points. Wait, the line passes through (60, 15)? Wait, no, maybe the red dot is (60, 15)? Wait, no, looking at the graph, the y-axis: 20 is above 0, -20 below. The red dot is at x=60, and y=15? Wait, maybe I made a mistake. Wait, let's re-express. Wait, the point-slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope.

First, find the slope. Let's take two points. Suppose the line goes through (60, 15) and another point. Wait, maybe the grid is 5 units per square. Wait, from x=60, if we move left 10 units (2 squares) to x=50, what's y? Wait, no, maybe the slope is 3? Wait, no, let's check the vertical change. Wait, maybe the line has a slope of 3. Wait, let's see: from x=60, y=15, if we go down 30 (6 squares) to y= -15, x would be 60 - 10 = 50? No, that doesn't make sense. Wait, maybe the slope is 3. Wait, maybe the point is (60, 15), and the slope is 3. Wait, no, let's do it properly.

Wait, the graph: the x-axis is from -100 to 100, y-axis from -100 to 20. The line is steep, so slope is large. Wait, maybe each grid square is 5 units. So x=60, y=15 (red dot). Let's find another point. If we move left 10 units (x=50), y would be 15 - 3*10 = -15? No, that's not right. Wait, maybe the slope is 3. Wait, let's calculate the slope. Suppose the line passes through (60, 15) and (50, -15). Then the slope \( m = \frac{-15 - 15}{50 - 60} = \frac{-30}{-10} = 3 \). So slope m=3. Then point-slope form is \( y - 15 = 3(x - 60) \). Wait, but maybe the point is (60, 15) and slope 3. Wait, but let's confirm.

Wait, maybe the red dot is (60, 15), and the slope is 3. So the point-slope form is \( y - 15 = 3(x - 60) \). But maybe I made a mistake. Wait, let's check the vertical change. If x increases by 10, y increases by 30 (since slope 3: 3*10=30). So from x=60, y=15, x=70, y=45. That seems steep, but the graph shows a steep line. So yes, slope 3, point (60,15). So point-slope form is \( y - 15 = 3(x - 60) \).

Wait, but maybe the point is (60, 15) and slope 3. So the equation is \( y - 15 = 3(x - 60) \).

Step1: Identify the point

The red dot is at \( (x_1, y_1) = (60, 15) \).

Step2: Calculate the slope

Let's find the slope \( m \). Take two points on the line. Suppose the line passes through \( (60, 15) \) and \( (50, -15) \). Then:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-15 - 15}{50 - 60} = \frac{-30}{-10} = 3 $$

Step3: Write point - slope form

Using point - slope formula \( y - y_1 = m(x - x_1) \), substitute \( x_1 = 60 \), \( y_1 = 15 \), and \( m = 3 \):

$$ y - 15 = 3(x - 60) $$

Answer:

\( y - 15 = 3(x - 60) \) (assuming the point is (60, 15) and slope 3; actual calculation may vary based on grid scale, but this is a possible solution)