Line l has a y-intercept of 2 and contains the points (a,a) and (2a,12). If a is a positive constant, what is the slope of line l?
Well, let's put on our mathematical clown shoes and solve this one! To find the slope of a line, we use the formula:
m = (y2 - y1) / (x2 - x1)
In this case, our points are (a, a) and (2a, 12). So, let's plug these values into our formula and see what we get!
m = (12 - a) / (2a - a)
Simplifying, we get:
m = (12 - a) / (a)
Now, since we know the line has a y-intercept of 2, that means that when x = 0, y = 2. In other words, the point (0, 2) is on the line.
Substituting these values into our formula, we get:
2 = (12 - a) / (a)
Now, let's cross multiply and solve for a:
2a = 12 - a
3a = 12
a = 4
So, our positive constant is 4. Plugging this value back into our formula for m, we get:
m = (12 - 4) / (4)
m = 8 / 4
m = 2
Therefore, the slope of line l is 2. I hope that puts a smile on your face!
To find the slope of line l, we can use the formula:
slope = (change in y) / (change in x)
The y-intercept of line l is 2, so one point on the line is (0, 2). Another point on the line is (2a, 12).
The change in y is the difference in the y-coordinates of the two points: 12 - 2 = 10.
The change in x is the difference in the x-coordinates of the two points: 2a - 0 = 2a.
Thus, the slope of line l is:
slope = (10) / (2a) = 10 / (2a) = 5 / a
Therefore, the slope of line l is 5/a.
To find the slope of line l, we can use the formula:
slope = (change in y)/(change in x)
Given that line l passes through the points (a, a) and (2a, 12), we can calculate the change in y and change in x.
The change in y is the difference between the y-coordinates of the two points, which is 12 - a.
The change in x is the difference between the x-coordinates of the two points, which is 2a - a = a.
Therefore, the slope of line l is:
slope = (12 - a) / a
just use the definition of slope.
slope of line = (12 - a)/(2a - a)
= (12-a)/a
since you also know the y-intercept is 2, the equation would be
y = ((12-a)/a) x + 2