Final answer:
To write an equation in slope-intercept form of the line that passes through two given points, find the slope and y-intercept. The equation is y = (7/3)x - 9.
Step-by-step explanation:
To write an equation in slope-intercept form of the line that passes through two given points, we need to find the slope (m) and the y-intercept (b). The formula for slope is (y2 - y1) / (x2 - x1). Using the points (6,3) and (3,10), we have (10 - 3) / (3 - 6) = -7 / -3 = 7/3. Now, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, we get y = (7/3)x + b. To find b, we can use one of the given points. Let's use (6,3): 3 = (7/3)(6) + b. Solving for b, we have b = -9. Therefore, the equation in slope-intercept form is y = (7/3)x - 9.
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