Claudia starts a new job, this time painting a fence at a steady rate. She paints all morning and then goes to lunch. The graph shows her progress after she returns from lunch.

Question

The X line goes from1 to 9
The y line goes from 4 to 36

The 3 points are on

Point 1
X 2
Y 8

Point 2 in on

X 4
Y 12

Point 3 is on

X 6
Y 16

The cordnites of the y intercept are what

Answer 1

To determine the coordinates of the y-intercept from the points provided, we need to analyze the points given in the problem.

The points provided are:

• Point 1: (2, 8)
• Point 2: (4, 12)
• Point 3: (6, 16)

Typically, to find the y-intercept of a linear function represented by a graph, we would look for where the line crosses the y-axis (where \(x = 0\)). However, since you only provided the points after lunch, we can derive the equation of the line defined by these points to find the y-intercept.

The points suggest a linear relationship since they seem to follow a pattern. We can calculate the slope (m) using the change in y over the change in x between any two points.

Using Point 1 and Point 2:

• \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{4 - 2} = \frac{4}{2} = 2 \)

The slope of the line is \( 2 \).

Next, we can use the point-slope form of the linear equation: \[ y - y_1 = m(x - x_1) \]

Let's use Point 1 (2, 8): \[ y - 8 = 2(x - 2) \]

Expanding this: \[ y - 8 = 2x - 4 \] \[ y = 2x + 4 \]

This is the equation of the line. To find the y-intercept, we substitute \(x = 0\): \[ y = 2(0) + 4 = 4 \]

So, the coordinates of the y-intercept are: (0, 4).