To graph the line that passes through the points (9,8) and (6,4), we find the slope and y-intercept, and then write the equation of the line as y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation is y = (4/3)x - 4.
Step-by-step explanation:
To graph the line that passes through the points (9,8) and (6,4), we can use the formula for the equation of a straight line: y = mx + b, where m is the slope of the line and b is the y-intercept.
Let's find the slope first by using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, m = (4 - 8) / (6 - 9) = -4 / -3 = 4/3.
Now, we can plug in one of the points, (9,8), into the equation y = mx + b to find the value of b. By substituting x = 9 and y = 8, we get 8 = (4/3)(9) + b. Solving for b, we get b = 8 - (4/3)(9) = 8 - 12 = -4.
Therefore, the equation of the line is y = (4/3)x - 4.