Final answer:
The rate of change, or slope, of the given function is 2. The y-intercept is -10, and both the domain and range are all real numbers. The graph of this linear function can be drawn by starting at the y-intercept and following the slope.
Step-by-step explanation:
The rate of change of a function in mathematics is also known as the slope of the line. Given the point-slope form y - y1 = m(x - x1), where m stands for the slope of the line, and the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can identify the rate of change.
For the equation provided in point-slope form y - 0 = 2(x - 5), the slope m is 2. This means that for each unit increase in x, y increases by 2 units. The intercept here indicates that when x is 5, y is at 0. If you convert the point-slope form to slope-intercept form (y = mx + b), you would get y = 2x - 10, confirming the slope is 2 and the y-intercept is -10.
To graph this function, you would start by plotting the y-intercept at (0, -10) on the y-axis. Then, from that point, you can use the slope to find another point: rise over run, moving up 2 units on the y-axis for every 1 unit you move right on the x-axis. Draw a straight line through these points to represent the linear function.
The domain of this function is all real numbers since there is no restriction on the x-values for a linear function. Likewise, the range is also all real numbers because as x goes to infinity in either direction, y will also cover all real values. The x-intercept can be found by setting y to 0 and solving for x, which gives x = 5.