Final answer:
To find the equation in slope-intercept form, we can calculate the slope using the given points and use one of the points to find the y-intercept. The equation of the line is y = 2x + 11.
Step-by-step explanation:
To find the equation of the line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
We can calculate the slope by using the formula: m = (y2 - y1) / (x2 - x1). So, for the points (2, 15) and (5, 21), the slope is: m = (21 - 15) / (5 - 2) = 2.
Now, we can substitute the slope (m) and one of the points (x, y) into the slope-intercept form to find the y-intercept (b). Using the point (2, 15): 15 = (2)(2) + b. Solving for b, we get: b = 11.
Therefore, the equation of the line in slope-intercept form is: y = 2x + 11.
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