Final answer:
The equation of the line passing through the points (5, 20) and (3, 12) in slope-intercept form is y = 4x.
Step-by-step explanation:
To find the equation of the line passing through the points (5, 20) and (3, 12) in slope-intercept form, we first need to find the slope of the line. The slope, denoted as 'm', can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates from the two points into the formula, we get:
m = (12 - 20) / (3 - 5) = -8 / -2 = 4
So the slope of the line is 4. Now, we can use the slope-intercept form of the equation, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Since we already have the value of 'm' (4), we can substitute one of the given points (for example, (5, 20)) into the equation to solve for 'b'.
20 = 4(5) + b
20 = 20 + b
b = 0
Therefore, the equation of the line passing through the points (5, 20) and (3, 12) in slope-intercept form is:
y = 4x