Final answer:
To write the equation in slope-intercept form, first find the slope using the formula (y2 - y1) / (x2 - x1), then choose a point and use the slope-intercept form equation y = mx + b.
Step-by-step explanation:
To write an equation in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
Given the points (2,3) and (-4,9), we can find the slope using the formula (y2 - y1) / (x2 - x1). Plugging in the values, we get (9 - 3) / (-4 - 2) = 6 / -6 = -1.
Next, we can choose either of the given points and substitute the values of x, y, and the slope into the slope-intercept form equation y = mx + b. Using the point (2,3), we have 3 = -1(2) + b. Solving for b, we get b = 5.
Therefore, the equation in slope-intercept form is y = -x + 5.