Question

The line represents the relationship between x, the number of hours it takes the painting company to finish the house, and y, the total cost of painting the house. What is the slope of the line Use the formula: (y2-y1) divided by ( x2-x1)

Answer 1

The slope of a line is the rate of change, calculated as 'rise over run' using two points on the line, and for the given equation y = 55x + 75, the slope is 55.

Step-by-step explanation:

The slope of a line describes the rate of change between the independent variable (x) and the dependent variable (y). To find the slope, you take two points on the line, designated as (x1, y1) and (x2, y2), and use the formula (y2-y1) divided by (x2-x1), which is often referred to as the 'rise over run'.

For example, in the given equation y = 55x + 75, the slope is the coefficient of x, which is 55. This means for every hour worked (increase in x), the total cost (y) increases by $55. The y-intercept is the value of y when x equals zero, and in this instance, it is 75, representing the initial cost before any labor is added.