To find the linear function represented by the point-slope equation y – 7 = 2/3 (x – 6), we need to transform this equation into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Start by distributing the 2/3 on the right side:
y – 7 = 2/3 * (x – 6)
y – 7 = 2/3 x – 2/3 * 6
y – 7 = 2/3 x – 4
Next, add 7 to both sides to isolate y:
y = 2/3 x – 4 + 7
y = 2/3 x + 3
Now, we have converted the point-slope equation into the slope-intercept form. Therefore, the linear function that represents this line is:
y = 2/3 x + 3