Final answer:
To write the slope-intercept form of the equation of a line, we can use the formula y = mx + b. For this line with a slope of -2/3 and containing the point (-6, 7), the equation is y = -2/3x + 3.
Step-by-step explanation:
To write the slope-intercept form of the equation of a line that contains the point (-6, 7) and has a slope of -2/3, we can use the formula y = mx + b. Here, m represents the slope and b represents the y-intercept. Since we have the slope and a point on the line, we can substitute these values into the equation.
Substituting the values, we have 7 = -2/3(-6) + b. Simplifying, we get 7 = 4 + b. To isolate b, we subtract 4 from both sides, giving us b = 3.
Therefore, the equation of the line in slope-intercept form is y = -2/3x + 3. The slope of the line is -2/3 and the y-intercept is 3.