Final answer:
To write the equation in slope-intercept form, we need to find the slope and the y-intercept. Using the given points (6,3) and (3,10), we can find the slope as -7/3. Substituting the slope and one of the points into the slope-intercept form equation, we can find the y-intercept as 17. Therefore, the equation of the line is y = (-7/3)x + 17.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need the slope and the y-intercept.
Given the points (6,3) and (3,10), we can find the slope using the formula:
Slope (m) = (change in y) / (change in x) = (10 - 3) / (3 - 6) = 7 / -3 = -7/3
Now, we can substitute the slope and one of the points, (6,3), into the slope-intercept form equation y = mx + b:
3 = (-7/3)(6) + b
To find the y-intercept, we solve for b:
3 = (-7/3)(6) + b
3 = -14 + b
b = 17
Therefore, the equation of the line is y = (-7/3)x + 17.