Final answer:
The equation of the line that passes through the points (-3, 8) and (1, 4) is y = -x + 5.
Step-by-step explanation:
To write the equation of the line that passes through the points (-3, 8) and (1, 4), you first need to calculate the slope of the line. The slope (m) is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the points (-3, 8) and (1, 4), the slope is calculated as follows:
m = (4 - 8) / (1 - (-3)) = -4 / 4 = -1
Next, use the slope and one of the points to write the equation in point-slope form: y - y1 = m(x - x1). Using the point (-3, 8) and the slope m = -1, the equation is:
y - 8 = -1(x - (-3))
Now, simplify and convert this into slope-intercept form (y = mx + b):
y - 8 = -1(x + 3)
y - 8 = -1x - 3
y = -1x + 5
The equation of the line is y = -x + 5.