Final answer:
The point-slope form of the line through (4, -2) with slope 5/3 is y + 2 = 5/3(x - 4).
Step-by-step explanation:
The equation of a line in point-slope form that passes through the point (4, -2) with a slope of 5/3 can be found using the point-slope formula y - y1 = m(x - x1). Plugging in the values, we have y + 2 = 5/3(x - 4). This equation demonstrates that for every three units the x-value (the run) increases, the y-value (the rise) will increase by five units, which is the 'rise over run' definition of slope.
When graphed, this line will cross the y-axis at the y-intercept, which is not directly given in this form but can be found by rearranging the equation into slope-intercept form.