a table has the points: (3, 8) (5, 11) (8, 15.5) (9, 17) (15, 26)

Answer 1

To find the equation of the curve represented by the given points, we can use the method of least squares to find a linear equation that best fits the data.

First, we need to calculate the slope of the line passing through the first and last points:

m = (y2 - y1) / (x2 - x1)
m = (26 - 8) / (15 - 3)
m = 18 / 12
m = 1.5

Next, we can use the point-slope form of a linear equation to find the y-intercept:

y - y1 = m(x - x1)
y - 8 = 1.5(x - 3)
y - 8 = 1.5x - 4.5
y = 1.5x + 3.5

Therefore, the equation of the curve represented by the given points is y = 1.5x + 3.5.

Answer 2

what is the slope?

Answer 3

The slope of the line passing through the given points is found by using the formula:

m = (change in y) / (change in x)

Taking two arbitrary points (x1, y1) and (x2, y2) from the given data, we can choose (3, 8) and (5, 11) to calculate the slope:

m = (11 - 8) / (5 - 3)
m = 3 / 2
m = 1.5

Therefore, the slope of the line passing through the given points is 1.5.

Answer 4

what does the y intercept represent on the graph?

Answer 5

In the context of a graph or a linear equation, the y-intercept represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.

For example, if a linear equation is given as y = mx + b, where m is the slope and b is the y-intercept, the y-intercept is the point on the y-axis where the graph of the equation crosses or intercepts the y-axis.

In simpler terms, the y-intercept represents the starting point of the graph when x = 0. This point is informative as it indicates a specific value of the dependent variable before any change in the independent variable occurs.