Answer:
To find the equation of a linear function given two points, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept.
Given the points (-1, 4) and (1, 7), we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the points into the formula, we have:
m = (7 - 4) / (1 - (-1))
m = 3 / 2
m = 1.5
Now that we have the slope, we can substitute one of the points and the slope into the slope-intercept form to find the value of b. Let's use the point (-1, 4):
4 = 1.5(-1) + b
4 = -1.5 + b
b = 4 + 1.5
b = 5.5
Therefore, the equation of the linear function passing through the points (-1, 4) and (1, 7) is:
y = 1.5x + 5.5
In conclusion, the equation of the linear function is y = 1.5x + 5.5.
Explanation: