Math / Geometry

QuestionActivity: 1) Pick any 2 points on the line (it's easier if you pick points on an intersection of grid lines) in grid Count the vertical distance 2) Cuares between the points: 3) Count the horizontal $\longleftrightarrow$ distance in grid squares between the points. 4) Slope $=\frac{\text { vertical distance }}{\text { horizontal distance }}=$ $\qquad$ 5)
Look at your neighbour's notes. Did they choose the same points? How do your slopes compare?

Studdy Solution

STEP 1

1. The line passes through the origin $(0,0)$ and another point $(5,5)$ .
2. The slope of a line is calculated as the ratio of the vertical change to the horizontal change between two points on the line.

STEP 2

1. Identify two points on the line.
2. Calculate the vertical distance between the points.
3. Calculate the horizontal distance between the points.
4. Compute the slope using the formula.
5. Compare slopes with a neighbor's calculation.

STEP 3

Identify two points on the line. In this case, the points are $(0,0)$ and $(5,5)$ .

STEP 4

Calculate the vertical distance between the points:
The vertical distance is the difference in the y-coordinates of the points: $\text{Vertical distance} = 5 - 0 = 5$

STEP 5

Calculate the horizontal distance between the points:
The horizontal distance is the difference in the x-coordinates of the points: $\text{Horizontal distance} = 5 - 0 = 5$

STEP 6

Compute the slope using the formula:
$\text{Slope} = \frac{\text{Vertical distance}}{\text{Horizontal distance}} = \frac{5}{5} = 1$

STEP 7

Compare slopes with a neighbor's calculation:
If your neighbor chose different points on the same line, the slope should still be $1$ , as the slope of a line is constant regardless of the points chosen.
The slope of the line is:
$\boxed{1}$

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Studdy Solution

STEP 1

1. The line passes through the origin $(0,0)$ and another point $(5,5)$ .
2. The slope of a line is calculated as the ratio of the vertical change to the horizontal change between two points on the line.

STEP 2

1. Identify two points on the line.
2. Calculate the vertical distance between the points.
3. Calculate the horizontal distance between the points.
4. Compute the slope using the formula.
5. Compare slopes with a neighbor's calculation.

STEP 3

Identify two points on the line. In this case, the points are $(0,0)$ and $(5,5)$ .

STEP 4

Calculate the vertical distance between the points:
The vertical distance is the difference in the y-coordinates of the points: $\text{Vertical distance} = 5 - 0 = 5$

STEP 5

Calculate the horizontal distance between the points:
The horizontal distance is the difference in the x-coordinates of the points: $\text{Horizontal distance} = 5 - 0 = 5$

STEP 6

Compute the slope using the formula:
$\text{Slope} = \frac{\text{Vertical distance}}{\text{Horizontal distance}} = \frac{5}{5} = 1$

STEP 7

Compare slopes with a neighbor's calculation:
If your neighbor chose different points on the same line, the slope should still be $1$ , as the slope of a line is constant regardless of the points chosen.
The slope of the line is:
$\boxed{1}$

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Studdy Solution

STEP 1

1. The line passes through the origin (0,0)(0,0)(0,0) and another point (5,5)(5,5)(5,5).2. The slope of a line is calculated as the ratio of the vertical change to the horizontal change between two points on the line.

STEP 2

1. Identify two points on the line.2. Calculate the vertical distance between the points.3. Calculate the horizontal distance between the points.4. Compute the slope using the formula.5. Compare slopes with a neighbor's calculation.

STEP 3

Identify two points on the line. In this case, the points are (0,0)(0,0)(0,0) and (5,5)(5,5)(5,5).

STEP 4

Calculate the vertical distance between the points:The vertical distance is the difference in the y-coordinates of the points: Vertical distance=5−0=5 \text{Vertical distance} = 5 - 0 = 5 Vertical distance=5−0=5

STEP 5

Calculate the horizontal distance between the points:The horizontal distance is the difference in the x-coordinates of the points: Horizontal distance=5−0=5 \text{Horizontal distance} = 5 - 0 = 5 Horizontal distance=5−0=5

STEP 6

Compute the slope using the formula:Slope=Vertical distanceHorizontal distance=55=1 \text{Slope} = \frac{\text{Vertical distance}}{\text{Horizontal distance}} = \frac{5}{5} = 1 Slope=Horizontal distanceVertical distance​=55​=1

STEP 7

Compare slopes with a neighbor's calculation:If your neighbor chose different points on the same line, the slope should still be 111, as the slope of a line is constant regardless of the points chosen. The slope of the line is:1 \boxed{1} 1​

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1. The line passes through the origin $(0,0)$ and another point $(5,5)$ .
2. The slope of a line is calculated as the ratio of the vertical change to the horizontal change between two points on the line.

1. Identify two points on the line.
2. Calculate the vertical distance between the points.
3. Calculate the horizontal distance between the points.
4. Compute the slope using the formula.
5. Compare slopes with a neighbor's calculation.

Identify two points on the line. In this case, the points are $(0,0)$ and $(5,5)$ .

Calculate the vertical distance between the points:
The vertical distance is the difference in the y-coordinates of the points: $\text{Vertical distance} = 5 - 0 = 5$

Calculate the horizontal distance between the points:
The horizontal distance is the difference in the x-coordinates of the points: $\text{Horizontal distance} = 5 - 0 = 5$

Compute the slope using the formula:
$\text{Slope} = \frac{\text{Vertical distance}}{\text{Horizontal distance}} = \frac{5}{5} = 1$

Compare slopes with a neighbor's calculation:
If your neighbor chose different points on the same line, the slope should still be $1$ , as the slope of a line is constant regardless of the points chosen.
The slope of the line is:
$\boxed{1}$