Solved on Jan 26, 2024

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

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

Calculate the difference in the y-coordinates.
$y_2 - y_1 = 6 - 7 = -1$

STEP 6

Calculate the difference in the x-coordinates.
$x_2 - x_1 = 4 - 8 = -4$

STEP 7

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

STEP 8

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

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

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

Calculate the difference in the y-coordinates.
$y_2 - y_1 = 6 - 7 = -1$

STEP 6

Calculate the difference in the x-coordinates.
$x_2 - x_1 = 4 - 8 = -4$

STEP 7

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

STEP 8

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

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

STEP 1

STEP 2

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

STEP 4

Substitute the coordinates of the points into the slope formula.m=6−74−8m = \frac{6 - 7}{4 - 8}m=4−86−7​

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

Simplify the fraction to get the slope in its simplest form.m=14m = \frac{1}{4}m=41​The slope of the line that passes through (8,7)(8,7)(8,7) and (4,6)(4,6)(4,6) is 14\frac{1}{4}41​.

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

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

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

Calculate the difference in the y-coordinates.
$y_2 - y_1 = 6 - 7 = -1$

Calculate the difference in the x-coordinates.
$x_2 - x_1 = 4 - 8 = -4$

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

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