Answer:
f(x) = 1/2x + 4
Explanation:
We can find a linear equation from two points using the slope-intercept form (y = mx + b), where m is the slope and b is the intercept
Step 1: First, we need to know what our two points by extracting it from the info we're given:
- We're told that f(-2) = 3 and since f(x) = y, the coordinate in (x, y) form is (-2, 3).
- Similarly, since f(4) = 6 the coordinate is (4, 6)
Step 2: We can find the slope using the slope formula, which is
m = (y2 - y1) / (x2 - x1), where (x1, y1) are one point on the line and (x2, y2) are another point.
- If we allow (-2, 3) to be our (x1, y1) point and (4, 6) to be our (x2, y2) point, we can find the slope:
m = (6 - 3) / (4 - (-2))
m = 3 / (4 + 2)
m = 3/6
m = 1/2 or m = 0.5
Step 3: We can find the y-intercept by plugging in one of the points for x and y and the slope we just found in the slope-intercept form. Then, we'll need to solve for b to get our y-intercept
Let's try our (x1, y1) point, namely (-2, 3)
3 = 1/2 (-2) + b
3 = -1 + b
4 = b
Thus, the linear equation that represents f(-2) = 3 and f(4) = 6 is:
f(x) = 1/2x + 4
Optional Step 4:
We can check that the equation we found is correct by plugging in f(-2) for x and see if we get 3 for y and by plugging in f(4) for x and seeing if we get 6
Checking equation accuracy with f(-2) = 3:
3 = 1/2 (-2) + 4
3 = -1 + 4
3 = 3
Checking equation accuracy with f(4) = 6:
6 = 1/2 (4) + 4
6 = 2 + 4
6 = 6