Final answer:
To find the equation of a line with a given slope and a point it passes through, insert the values into the slope-intercept form and solve for the y-intercept. The equation of the line with slope 8/3 and passing through the point (9,7) is y = (8/3)x - 17.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we can use the given slope m = 8/3 and the point it passes through, which is (9,7). First, we substitute the slope and the coordinates of the point into the slope-intercept equation to find b:
- y = mx + b
- 7 = (8/3)(9) + b
- 7 = 24 + b
- b = 7 - 24
- b = -17
The equation of the line is therefore y = (8/3)x - 17.