A line has a slope of 3/5. Through which two points could this line pass?
To find two points through which the line could pass, we need the values of the x and y coordinates. Let's choose the y-coordinate values as 0 and 5 to make the calculations easier:
When y = 0:
y = mx + b (where m is the slope)
0 = (3/5)x + b
0 = 3x + 5b ... multiplying both sides by 5 to eliminate the fraction
When y = 5:
5 = (3/5)x + b
25 = 3x + 5b ... multiplying both sides by 5 to eliminate the fraction
We now have a system of equations:
0 = 3x + 5b
25 = 3x + 5b
Since these two equations are equal, they represent the same line and it passes through any points that satisfy both equations. Let's solve for x:
0 = 3x + 5b ...equation 1
25 = 3x + 5b ...equation 2
Subtract equation 1 from equation 2:
25 - 0 = 3x + 5b - (3x + 5b)
25 = 0
This equation is not possible. Therefore, a line with a slope of 3/5 cannot pass through a pair of points with y-coordinate values of 0 and 5.