Final answer:
The equation of the linear function passing through the points (-4, 13) and (8, 4) is y = (-3/4)x + 10, determined by calculating the slope and y-intercept of the line connecting the points.
Step-by-step explanation:
To find an equation of the linear function whose graph passes through the points (-4, 13) and (8, 4), we first need to calculate the slope of the line (m) that connects these points.
The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points, we get:
m = (4 - 13) / (8 - (-4)) = -9 / 12 = -3 / 4
The slope of the line is -3/4. Next, we use the slope and one of the points to find the y-intercept (b) of our line using the point-slope form of a linear equation, which is y - y1 = m(x - x1).
Using point (-4, 13), we get:
13 - (-3/4)(-4) = 13 - 3 = 10
Thus, the y-intercept is 10. Now we can express the equation of the line in slope-intercept form, which is y = mx + b.
Therefore, the equation of the line is:
y = (-3/4)x + 10.