Final answer:
To find the equation of a line in slope-intercept form, we need to find the slope and the y-intercept using the given points. The slope is the change in y divided by the change in x, while the y-intercept is the value of y when x is 0. Plugging in the values from the given points, the equation of the line is y = (1/3)x - 2/3.
Step-by-step explanation:
To write the equation of the line in slope-intercept form, we need to find the slope (m) and the y-intercept (b). The formula for finding the slope is: m = (y2 - y1) / (x2 - x1). Using the points (-4, -2) and (14, 4), we can substitute the values into the formula: m = (4 - (-2)) / (14 - (-4)) = 6/18 = 1/3. Now that we have the slope, we can find the y-intercept, which is the value of y when x = 0. Using the point (-4, -2), we substitute x = 0 into the slope-intercept form equation: y = mx + b. We have: -2 = (1/3)(-4) + b. Solving for b: b = -2 + 4/3 = -2/3. Therefore, the equation of the line is: y = (1/3)x - 2/3.
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