Find an equation of a linear function given h(1) = 6 and h(4) = –3.

Sure, let's find the equation of the linear function.

A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Find the slope (m) The slope can be found using the formula m = (y2 - y1) / (x2 - x1). Here, we have two points (1, 6) and (4, -3). So, x1 = 1, y1 = 6, x2 = 4, and y2 = -3.

Substitute these values into the formula: m = (-3 - 6) / (4 - 1) = -9 / 3 = -3

Step 2: Find the y-intercept (b) We can find b by substituting the slope and one of the points into the equation y = mx + b. Let's use the point (1, 6).

6 = -3*1 + b 6 = -3 + b b = 6 + 3 = 9

So, the equation of the linear function is h(x) = -3x + 9.