Final answer:
To write the equation in slope-intercept form, we first find the slope using the given points, and then substitute the slope and one point into the equation y = mx + b to find the y-intercept. The equation in slope-intercept form that passes through (7, -2) and (21, -14) is y = (-6/7)x + 4.
Step-by-step explanation:
To write an equation in slope-intercept form, we will use the formula: y = mx + b, where m is the slope and b is the y-intercept. Let's find the slope first. The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1). Using the given points (7, -2) and (21, -14), we substitute the values into the formula: m = (-14 - (-2)) / (21 - 7) = -12 / 14 = -6 / 7. Now, we have the slope (-6/7), and we can substitute this value along with one of the given points into the equation y = mx + b to find the y-intercept (b). Using the point (7, -2), we substitute the values into the equation: -2 = (-6/7)(7) + b. Simplifying this equation, we get: -2 = -6 + b. Finally, adding 6 to both sides of the equation, we get: -2 + 6 = b, which gives us b = 4. Therefore, the equation in slope-intercept form that passes through the given points is: y = (-6/7)x + 4.
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