Final answer:
The equation in slope-intercept form for the line that passes through the point (-4, 2) and has a slope of -9/2 is y = -9/2x + 20.
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 equation of a line given a point and a slope, we can plug the values into the slope-intercept form and solve for b.
In this case, the slope m is -9/2 and the point is (-4, 2). Plugging these values into the slope-intercept form, we get: y = -9/2x + b.
Now, substitute the coordinates of the point (-4, 2) into the equation and solve for b. We have: 2 = -9/2(-4) + b. Solving for b, we get: b = 20.
Therefore, the equation in slope-intercept form for the line that passes through the point (-4, 2) and has a slope of -9/2 is y = -9/2x + 20.