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Math

Question Find the slope of the line passing through (8,7) and (4,6). Express the answer as a fraction or integer.

Studdy Solution

STEP 1

Assumptions
1. The line passes through the points (8,7)(8,7) and (4,6)(4,6).
2. We need to find the slope of the line.
3. The slope (m) of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

STEP 2

Identify the coordinates of the two given points. Let (x1,y1)=(8,7)(x_1, y_1) = (8, 7) and (x2,y2)=(4,6)(x_2, y_2) = (4, 6).

STEP 3

Use the slope formula to find the slope of the line passing through the two points.
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

STEP 4

Substitute the coordinates of the points into the slope formula.
m=6−74−8m = \frac{6 - 7}{4 - 8}

STEP 5

Calculate the difference in the y-coordinates.
y2−y1=6−7=−1y_2 - y_1 = 6 - 7 = -1

STEP 6

Calculate the difference in the x-coordinates.
x2−x1=4−8=−4x_2 - x_1 = 4 - 8 = -4

STEP 7

Now, calculate the slope using the differences obtained.
m=−1−4m = \frac{-1}{-4}

STEP 8

Simplify the fraction to get the slope in its simplest form.
m=14m = \frac{1}{4}
The slope of the line that passes through (8,7)(8,7) and (4,6)(4,6) is 14\frac{1}{4}.

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