Final answer:
The line with a slope that goes down 2 units and right 1 unit through the point (4, 5) can be represented by the equation y = -2x + 13, where -2 is the slope and 13 is the y-intercept.
Step-by-step explanation:
To draw a line through the point (4, 5) with a slope that goes down 2 units and right 1 unit, you begin at (4, 5) and move 2 units down and 1 unit to the right to mark another point. Given that the point (5, 3) also lies on this line, we can confirm that the slope is indeed -2 (since from (4, 5) to (5, 3) you move down 2 and right 1). The slope of the line, therefore, is -2/1, or simply -2.
To write the equation of this line, we use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Since we have a slope (m) and a point (4, 5) we use these to solve for the y-intercept (b). After substituting the point into the equation (5 = -2(4) + b), we find that the y-intercept b = 13.
The equation of the line is y = -2x + 13.
This demonstrates how the m and b terms in an equation for a straight line determine the line's slope and y-intercept, respectively. In this case, m = -2 shows the slope, and b = 13 is the point where the line crosses the y-axis.