Final answer:
To write the equation in slope-intercept form, we find the slope using the given points and substitute it into the equation. By solving for the y-intercept, we obtain the equation y = -x + 5.
Step-by-step explanation:
To write an equation in slope-intercept form, we need to use the formula y = mx + b. We can find the slope (m) by using the formula m = (y2 - y1) / (x2 - x1). Using the points (2, 3) and (-4, 9), we can substitute the values into the formula to find the slope. Once we have the slope, we can substitute one of the points and the slope into the slope-intercept form equation to find the y-intercept (b).
For the given points, the slope is (3 - 9) / (2 - (-4)) = -6 / 6 = -1. Using the point (2, 3), we can substitute the slope (-1) and the point into the equation y = mx + b and solve for the y-intercept (b). Plugging in the values, we get 3 = -1(2) + b. Solving for b, we find that b = 5. Therefore, the equation in slope-intercept form is y = -x + 5 or y = -1x + 5.
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