Answer:
Explanation:
To write a linear equation in slope-intercept form (y = mx + b) that satisfies the given conditions, we need to find both the slope (m) and the y-intercept (b).
Given conditions:
1. When x = 2, y = 1 (F(2) = 1)
2. When x = -3, y = 7 (F(-3) = 7)
Let's find the slope (m) first:
\[m = \frac{\text{change in } y}{\text{change in } x} = \frac{7 - 1}{-3 - 2} = \frac{6}{-5}\]
Now that we have the slope, let's use the point-slope form of a linear equation to find the equation:
\[y - y_1 = m(x - x_1)\]
Using the point (2, 1):
\[y - 1 = \frac{6}{-5}(x - 2)\]
Now, we can simplify and rearrange it into the slope-intercept form:
\[y - 1 = -\frac{6}{5}x + \frac{12}{5}\]
\[y = -\frac{6}{5}x + \frac{12}{5} + 1\]
Combining constants:
\[y = -\frac{6}{5}x + \frac{17}{5}\]
So, the linear equation in slope-intercept form that satisfies the given conditions is \(y = -\frac{6}{5}x + \frac{17}{5}\).