Question

How might you use the digits 0 thru 5 at most one time to write an equation where the rate of change is greater than 2, the y-intercept is less than your equation in slope-intercept form where m represents the rate of change and b represents the y-intercept (y=mx + b). List 2 points (x, y) from your line.

Answer 1

To write an equation with a slope greater than 2 and a y-intercept less than the equation in slope-intercept form, we can use the digits 0 to 5 at most one time. By assigning 3 to the slope (m) and 1 to the y-intercept (b), the equation y = 3x + 1 satisfies the given conditions. Two points on this line are (0, 1) and (1, 4).

Step-by-step explanation:

To write an equation with the given conditions, we need to consider the slope and the y-intercept. The slope needs to be greater than 2, and the y-intercept needs to be less than the equation in slope-intercept form (y = mx +b). We can use the digits 0 through 5 at most one time to determine the values for m and b.

1. Let's assign the digits 0 to 5 to represent potential values for m and b.
2. To satisfy the condition of the slope being greater than 2, we can choose m to be 3.
3. To satisfy the condition of the y-intercept being less than the equation in slope-intercept form, we can choose b to be 1.
4. Therefore, the equation that satisfies these conditions is y = 3x + 1.
5. Two points on this line can be obtained by substituting different values of x into the equation and solving for y. For example, when x = 0, y = 1; when x = 1, y = 4.