Final answer:
To write an equation in slope-intercept form, substitute the given slope and point coordinates into the formula and solve for the y-intercept. The equation of the line is y = (-3/2)x - 7.
Step-by-step explanation:
To write an equation in slope-intercept form, we can use the formula y = mx + b, where m is the slope and b is the y-intercept. Given that the line passes through the point (-6,2) and has a slope of -3/2, we can substitute these values into the equation.
Plugging in the values, we get: y = (-3/2)x + b. To find the value of b, we can substitute the coordinates of the given point: 2 = (-3/2)(-6) + b. Solving for b, we get b = -7. Therefore, the equation of the line in slope-intercept form is y = (-3/2)x - 7.