Final answer:
The slope-intercept form of the line passing through (9,2) and (-2,6) is y = (-4/11)x + (58/11), where -4/11 is the slope and 58/11 is the y-intercept.
Step-by-step explanation:
To write the equation of the line in slope-intercept form that passes through the points (9,2) and (-2,6), we need to first find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (6 - 2) / (-2 - 9), which simplifies to m = 4 / -11. The slope of our line is therefore -4/11.
Next, we use the slope-intercept form of the equation y = mx + b to find the y-intercept (b). We can use one of the points for this; let's use (9,2). We have 2 = (-4/11)9 + b. Solving for b, we get b = 2 + (4/11)9 = 2 + 36/11 = 58/11.
The equation of the line in slope-intercept form is therefore y = (-4/11)x + (58/11).