Write a rule for this function:
(-2,1), (0,4)
Also provide an explanation for how you got your answer. Thanks.
There are inifinitely many functions containing those two points. However, the simplest would be a line joining the two points.
The slope of that line is (4-1)/(0+2) = 3/2
Now, at any point (x,y) on the line, the slope of the line joining (x,y) and either of the points, say, (0,4) is also 3/2.
(y-4)/(x-0) = 3/2
y-4 = 3/2 x
y = 3/2 x + 4
2x3=6
To write a rule for the function given the points (-2, 1) and (0, 4), we need to find the relationship between the input values (x) and the output values (y).
Step 1: Find the difference between the x-values and the y-values for the two points:
-2 - 0 = -2
1 - 4 = -3
Step 2: Determine the ratio between the y-value difference and the x-value difference:
-3 / -2 = 1.5
Step 3: Write the rule using the calculated ratio and one of the points:
y = mx + b
Since the ratio is 1.5 and we have the point (-2, 1), we can substitute these values into the equation:
1 = 1.5(-2) + b
Simplifying this equation, we get:
1 = -3 + b
Step 4: Solve for the constant term (b):
b = 1 + 3
b = 4
Therefore, the rule for the given function is:
y = 1.5x + 4
Explanation:
To find the rule for the given function, we used the slope-intercept form of a linear equation (y = mx + b). First, we found the difference between the x-values and the y-values of the given points. Then, we determined the ratio between the y-value difference and the x-value difference. Substituting the calculated values and a specific point into the slope-intercept form, we solved for the constant term (b). This allowed us to write the rule of the function as y = 1.5x + 4.