4. Use information from number 3 to answer the following:
a. Extend your trend line so that it crossed the y-axis. Determine the y-intercept.
b. Determine the order pairs of two of the points that your trend line is passing through. Find the slope using the two points and the formula.
c. Write your equation in y=mx+b form.
Equation of trend line: __________________
a. To extend the trend line to cross the y-axis, we need to determine the y-intercept. From the information given in number 3, we know that the trend line passes through the point (2, 4). This point gives us the coordinates (x, y) = (2, 4). The y-intercept is the value of y when x=0. To find this, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Since we don't have the slope yet, let's determine it in part b first.
b. Let's choose two points on the trend line to find the slope using the formula. From the information given in number 3, let's choose the points (1, 2) and (3, 6). The coordinates of the first point are (x1, y1) = (1, 2) and the coordinates of the second point are (x2, y2) = (3, 6).
The slope formula is given by: slope = (y2 - y1) / (x2 - x1)
Plugging in the values, we have: slope = (6 - 2) / (3 - 1) = 4 / 2 = 2
Now that we have the slope, we can determine the y-intercept in part a.
a. To find the y-intercept, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We know the slope is 2 and we have the coordinates of a point on the line, (2, 4).
Plugging in the values, we have: 4 = 2(2) + b
Simplifying this equation, we get:
4 = 4 + b
Subtracting 4 from both sides, we find:
b = 0
Therefore, the y-intercept is 0. The trend line crosses the y-axis at (0, 0).
c. Now that we have the slope, m = 2, and the y-intercept, b = 0, we can write the equation of the trend line in y = mx + b form.
The equation of the trend line is: y = 2x + 0
Simplifying this equation, we have:
y = 2x
Therefore, the equation of the trend line is y = 2x.