Answer:the linear function f(x) with f(4) = -3 and f(0) = -2 is: f(x) = (-1/4)x - 2 This function represents a line with a slope of -1/4 and a y-intercept of -2.
Step-by-step explanation: To write a linear function, we can use the slope-intercept form, which is given by the equation: f(x) = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope (m), we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Using the points (4, -3) and (0, -2), we can substitute these values into the formula: m = (-3 - (-2)) / (4 - 0) = (-3 + 2) / 4 = -1 / 4 Now that we have the slope (m), we can substitute it into the slope-intercept form: f(x) = (-1/4)x + b To find the y-intercept (b), we can substitute the coordinates of any point on the line into the equation. Let's use the point (4, -3): -3 = (-1/4)(4) + b -3 = -1 + b b = -3 + 1 b = -2