To find the equation of a linear function in slope-intercept form from a table of values, you’ll need to determine the slope and the y-intercept of the line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
The table provided suggests a linear relationship between x and y with corresponding values. By examining the change in y over the change in x, we can determine the slope. For example, as x increases from 1 to 2, y increases from 2 to 12, which is a change of 10 in y for a change of 1 in x, giving us a slope of 10. To find the y-intercept (b), we can either extend the line back to where it crosses the y-axis (x=0) or use one of the points to solve for b in our slope-intercept equation.
Using the point (1, 2) and the calculated slope of 10, the intercept b can be calculated as follows: 2 = 10(1) + b, which gives us b = -8. Therefore, the equation of the linear function is y = 10x - 8.
Final answer is The equation of the linear function represented by the given table is y = 10x - 8, where the slope (m) is 10 and the y-intercept (b) is -8.