Final answer:
To find the equation in slope intercept form, find the slope using the formula, substitute the slope and one of the given points into the form, and solve for the y-intercept.
Step-by-step explanation:
To write the equation of a line in slope intercept form, you need to have the slope and the y-intercept. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, you can use the formula: m = (y2 - y1) / (x2 - x1).
Using the given points (6, -2) and (12, 1), we can calculate the slope:
m = (1 - (-2)) / (12 - 6) = 3/6 = 1/2
Now, substituting the slope (1/2) and one of the given points (6, -2) into the slope intercept form, we get y = (1/2)x + b. Plugging in the coordinates (6, -2), we can solve for b:
-2 = (1/2)(6) + b
-2 = 3 + b
b = -5
Therefore, the equation of the line is y = (1/2)x - 5.
Learn more about Writing line equations in slope intercept form