Final answer:
To find the equation of the line that passes through (-1,9) and (6,5), calculate the slope as -4/7, then use it with one of the points to determine the y-intercept as 59/7. The equation of the line is y = -4/7x + 59/7.
Step-by-step explanation:
To write the equation of a line that passes through the points (-1,9) and (6,5), we need to find the slope and use it to define the line's equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, calculate the slope by using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get the slope as:
m = (5 - 9) / (6 - (-1)) = (-4) / (7) = -4/7
Now, we use one of the points and the slope to solve for b. Using the point (-1,9):
9 = (-4/7)(-1) + b → b = 9 - 4/7 → b = 63/7 - 4/7 → b = 59/7
Thus, the equation of the line is:
y = -4/7x + 59/7