Final answer:
To write the equation of a line, find the slope using the formula and then solve for the y-intercept. Using the points (-2, -6) and (7, 18), the equation of the line is y = 8/3x - 2/3.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need to know the slope and the y-intercept. The slope of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The y-intercept is the value of y when x = 0.
Using the given points (-2, -6) and (7, 18), we can first find the slope:
m = (18 - (-6)) / (7 - (-2)) = 24/9 = 8/3
Next, we can substitute one of the points into the slope-intercept form equation y = mx + b to solve for the y-intercept:
-6 = (8/3)(-2) + b
Simplifying the equation, we get: -6 = -16/3 + b
Adding 16/3 to both sides, we have: b = -6 + 16/3 = -18/3 + 16/3 = -2/3
Therefore, the equation of the line in slope-intercept form is y = 8/3x - 2/3.
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