Final answer:
The equation of the line with a slope of -2/3 that passes through the point (6, -10) is y = (-2/3)x - 6.
Step-by-step explanation:
To write the equation of the line in slope-intercept form, which is y = mx + b, we need to use the given slope (m = -2/3) and the point through which the line passes (6, -10). We will substitute these values into the slope-intercept form to solve for the y-intercept (b).
The slope-intercept form of a line is given by:
y = mx + b
Let's substitute the point (6, -10) and the slope (-2/3) into this equation:
-10 = (-2/3)(6) + b
To find b, we will solve for it:
-10 = -4 + b
b = -10 + 4
b = -6
Now that we have b, the y-intercept, we can write the final equation of the line:
y = (-2/3)x - 6