A line connecting (2, 1) to another point has a slope of 3. What is the closest point with whole number coordinates above (2, 1)?
(2,1), (3,Y), m = 3.
m = (Y-1) / (3-2) = 3,
(Y-1) / 1 = 3,
Y - 1 = 3,
Y = 4.
(2,1),(3,4).
To find the closest point with whole number coordinates above (2, 1), we need to determine the equation of the line connecting these two points.
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope of the line is 3. So, the equation becomes y = 3x + b.
To find the y-intercept, we can substitute the coordinates (2, 1) into the equation:
1 = 3(2) + b
1 = 6 + b
b = 1 - 6
b = -5
Therefore, the equation of the line is y = 3x - 5.
Now, we need to find the point with whole number coordinates above (2, 1), which means the y-coordinate must be greater than 1.
Let's start by substituting x = 2 into the equation to find the y-coordinate:
y = 3(2) - 5
y = 6 - 5
y = 1
Since the y-coordinate is still 1, we need to increase the x-coordinate to find a point with a greater y-coordinate.
Let's substitute x = 3 into the equation to find the new y-coordinate:
y = 3(3) - 5
y = 9 - 5
y = 4
Therefore, the closest point with whole number coordinates above (2, 1) is (3, 4).
To find the point with whole number coordinates above (2, 1) that lies on a line with a slope of 3, we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by: y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) are the coordinates of a point on the line.
In this case, we have the coordinates (x1, y1) = (2, 1) and the slope m = 3, so the equation becomes: y - 1 = 3(x - 2).
To find the point with whole number coordinates above (2, 1), we can start substituting different values of x to solve for y.
Let's start with x = 3:
y - 1 = 3(3 - 2)
y - 1 = 3
y = 3 + 1
y = 4
Therefore, when x = 3, y = 4, so the closest point with whole number coordinates above (2, 1) is (3, 4).