Final answer:
The slope-intercept form of the equation for the line passing through (-9, -2) and (1, 3) is y = (1/2)x + 5/2.
Step-by-step explanation:
The slope-intercept form of an equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula (y2 - y1)/(x2 - x1). From the given points, (-9, -2) and (1, 3), we have a change in y of 3 - (-2) = 5, and a change in x of 1 - (-9) = 10. Therefore, the slope is 5/10 = 1/2.
Now, we substitute one of the given points, say (1, 3), into the equation y = mx + b to find the y-intercept. We have 3 = (1/2)(1) + b, which simplifies to b = 3 - 1/2 = 5/2.
Therefore, the slope-intercept form of the equation for this line is y = (1/2)x + 5/2.
Learn more about slope-intercept form of an equation