Final answer:
To find the equation of a line given a set of points, you calculate the slope (m) from any two points and find the y-intercept (b) by solving the line equation for b using one of the given points. The equation of the line provided in this example is y = -3.5x + 4.
Step-by-step explanation:
When we talk about the equation of a line in the form y = mx + b, m represents the slope of the line and b represents the y-intercept, the point where the line crosses the y-axis.
To find the slope (m), we look at the rate of change in the y values relative to the changes in the x values.
In the case of the data provided, we can calculate the slope by taking the change in y divided by the change in x between any two points.
Assuming the data presents a linear relation, if we take two points, say (2, -3) and (4, -10), the slope is calculated as (change in y) / (change in x) = (-10 - (-3)) / (4 - 2) = (-7) / (2) = -3.5.
The y-intercept (b) can be found by examining where the line would cross the y-axis. This can be done by substituting the slope and one point into the equation and solving for b.
If we use the point (2, -3), b can be found by plugging these values into the equation: -3 = (-3.5)(2) + b.
Solving this gives b = 4.
Therefore, the equation of the line in y = mx + b form is y = -3.5x + 4.