determine m given that m>0 and the points (m,3) and (1,m) lie on a line with slope m

Please use the subject area in the appropriate space so that the teachers know what help you need.

write the correct abbreviation for each metric init 1)kilogram 2)meter 3)Gram 4)milliliter 5)Millimeter 6)liter 7)kilometer 8)centimeter 9)Milligram

To determine the value of m, we can use the slope formula. The formula for slope (m) is:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

In this case, the given points are (m, 3) and (1, m). So, we can substitute these values into the slope formula:

m = (m - 3) / (1 - m)

Now, we can simplify the equation and solve for m. Let's start by cross-multiplying:

m(1 - m) = (m - 3)

Expanding the left side:

m - m^2 = m - 3

Moving all terms to one side:

m - m + 3 = m^2 - m

Rewriting the equation:

0 = m^2 - m

Rearranging the equation:

m^2 - m = 0

Now, we can factor out a common factor of m:

m(m - 1) = 0

This equation can be true if either m = 0 or (m - 1) = 0.

1) If m = 0, it satisfies the condition of m > 0, so it is a valid solution.

2) If (m - 1) = 0, then m = 1, which also satisfies the condition of m > 0.

Therefore, the values of m that satisfy the given conditions are m = 0 and m = 1.

To determine the value of m, given that the points (m,3) and (1,m) lie on a line with slope m, we can use the slope formula.

The slope formula is given by:
m = (y2 - y1) / (x2 - x1)

Let's label the coordinates of the two points:
Point A: (m, 3)
Point B: (1, m)

Substituting the coordinates into the slope formula, we have:
m = (m - 3) / (1 - m)

To eliminate the denominator, we can multiply both sides of the equation by (1 - m):
m(1 - m) = m - 3

Expanding the equation:
m - m^2 = m - 3

Rearranging terms to one side:
m^2 - 2m + 3 = 0

This is a quadratic equation. To solve for m, we can use the quadratic formula:
m = (-b ± √(b^2 - 4ac)) / (2a)

Comparing the equation to the quadratic formula, we have:
a = 1, b = -2, c = 3

Substituting the values into the quadratic formula, we get:
m = (-(-2) ± √((-2)^2 - 4(1)(3))) / (2(1))
m = (2 ± √(4 - 12)) / 2
m = (2 ± √(-8)) / 2

Since the problem statement states that m > 0, we cannot take the square root of a negative value. Therefore, there are no real solutions for m that satisfy the given conditions.

Hence, there is no value of m that satisfies m > 0 and the points (m,3) and (1,m) lying on a line with slope m.