Question

In the coordinate plane, line L has a slope of 3/5 and passes through point (-2, 6). Which of the following points also lies on line L

lewismadi

Answer 1

To find a point that lies on line L, we need to use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the slope of line L is 3/5. Using the point (-2, 6), we can plug in these values into the equation and solve for b.

6 = (3/5)(-2) + b
6 = -6/5 + b
To clear the fraction, we multiply both sides of the equation by 5:
30 = -6 + 5b
Add 6 to both sides:
36 = 5b
Divide by 5:
b = 36/5

So the equation of line L is y = (3/5)x + (36/5).

Now we can check which of the following points satisfy this equation:

a) (1, 4)
Plugging in x = 1 and y = 4 into the equation, we get:
4 = (3/5)(1) + (36/5)
4 = 3/5 + 36/5
4 = 39/5

Since 4 is not equal to 39/5, point (1, 4) does not lie on line L.

b) (-5, 2)
Plugging in x = -5 and y = 2 into the equation, we get:
2 = (3/5)(-5) + (36/5)
2 = -3 + 36/5
2 = -15/5 + 36/5
2 = 21/5

Since 2 is not equal to 21/5, point (-5, 2) does not lie on line L.

c) (4, 8)
Plugging in x = 4 and y = 8 into the equation, we get:
8 = (3/5)(4) + (36/5)
8 = 12/5 + 36/5
8 = 48/5

Since 8 is equal to 48/5, point (4, 8) lies on line L.

Therefore, the point (4, 8) is the only one that lies on line L.