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Math

Question Find the value of X2X^2 in the equation m=(2−(−7))((−4)−(−6))m=\frac{(2-(-7))}{((-4)-(-6))}.

Studdy Solution

STEP 1

Assumptions
1. We are given an equation in the form of a slope (m) of a line passing through two points.
2. The formula for the slope (m) is given by the difference in y-coordinates over the difference in x-coordinates of two points on the line.
3. The two points have coordinates (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), where x1=−4x_1 = -4, y1=2y_1 = 2, x2=−6x_2 = -6, and y2=−7y_2 = -7.
4. We need to calculate the value of the slope (m) using these points.

STEP 2

First, let's write down the formula for the slope (m) of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=(y2−y1)(x2−x1)m = \frac{(y_2 - y_1)}{(x_2 - x_1)}

STEP 3

Now, plug in the given values for x1x_1, y1y_1, x2x_2, and y2y_2 into the slope formula:
m=(−7−2)(−6−(−4))m = \frac{(-7 - 2)}{(-6 - (-4))}

STEP 4

Simplify the numerator (the difference in y-coordinates):
−7−2=−9-7 - 2 = -9

STEP 5

Simplify the denominator (the difference in x-coordinates):
−6−(−4)=−6+4=−2-6 - (-4) = -6 + 4 = -2

STEP 6

Now, substitute the simplified numerator and denominator back into the slope formula:
m=−9−2m = \frac{-9}{-2}

STEP 7

Calculate the slope (m) by dividing the numerator by the denominator:
m=−9−2=4.5m = \frac{-9}{-2} = 4.5
The slope of the line is 4.54.5.

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