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
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.
To identify which of the given points lies on line L, we need to use the slope-intercept form of a linear equation. The equation for a line with a slope of 3/5 passing through the point (-2, 6) is:
y - y1 = m(x - x1)
Where (x1, y1) is the point (-2, 6) and m is slope 3/5.
Plugging in the values we have:
y - 6 = (3/5)(x - (-2))
Simplifying the equation:
y - 6 = (3/5)(x + 2)
Next, we can distribute (3/5) to (x + 2):
y - 6 = (3/5)x + (6/5)
To isolate y, add 6 to both sides of the equation:
y = (3/5)x + (6/5) + 6
y = (3/5)x + (6/5) + (30/5)
y = (3/5)x + (36/5)
Now that we have the equation in slope-intercept form (y = mx + b), we can determine which of the given points satisfy this equation.
Let's check each point:
(a) (1, 4):
Substituting x = 1 and y = 4 into the equation:
4 = (3/5)(1) + (36/5)
4 = 3/5 + 36/5
4 = 39/5
The equation does not hold true for point (1, 4).
(b) (0, 6):
Substituting x = 0 and y = 6 into the equation:
6 = (3/5)(0) + (36/5)
6 = 36/5
The equation does not hold true for point (0, 6).
(c) (7, 12):
Substituting x = 7 and y = 12 into the equation:
12 = (3/5)(7) + (36/5)
12 = 21/5 + 36/5
12 = 57/5
The equation does not hold true for point (7, 12).
(d) (-3, 4):
Substituting x = -3 and y = 4 into the equation:
4 = (3/5)(-3) + (36/5)
4 = -9/5 + 36/5
4 = 27/5
The equation does not hold true for point (-3, 4).
Based on the analysis, none of the given points satisfy the equation for line L.
To determine which of the given points lies on line L, we can use the slope-intercept form of a linear equation:
y = mx + b
Where:
- m is the slope of the line
- (x, y) is a point on the line
- b is the y-intercept of the line
Given that line L has a slope of 3/5 and passes through point (-2, 6), we can substitute these values into the equation:
6 = (3/5)(-2) + b
Next, we can solve for b:
6 = -6/5 + b
To combine the fraction and the whole number, we need to find a common denominator. The common denominator here is 5, so we can rewrite 6 as 30/5:
30/5 = -6/5 + b
Now, we can add -6/5 to both sides to isolate b:
30/5 + 6/5 = b
(30 + 6)/5 = b
36/5 = b
So, the y-intercept of line L is 36/5.
Now, we can use the equation y = (3/5)x + 36/5 to check which of the given points also satisfies this equation.