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Sagot :
To find the slope of the line that crosses the coordinates [tex]\((-4, -5)\)[/tex] and [tex]\((2, 4)\)[/tex], we use the formula for the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's apply this formula step-by-step with our given points:
1. Identify the coordinates:
- [tex]\((x_1, y_1) = (-4, -5)\)[/tex]
- [tex]\((x_2, y_2) = (2, 4)\)[/tex]
2. Substitute these values into the slope formula:
[tex]\[ m = \frac{4 - (-5)}{2 - (-4)} \][/tex]
3. Simplify the numerator and the denominator:
- Numerator: [tex]\(4 - (-5) = 4 + 5 = 9\)[/tex]
- Denominator: [tex]\(2 - (-4) = 2 + 4 = 6\)[/tex]
4. Divide the simplified numbers:
[tex]\[ m = \frac{9}{6} \][/tex]
5. Reduce the fraction to its simplest form:
[tex]\[ \frac{9}{6} = \frac{3}{2} \][/tex]
Therefore, the slope of the line that crosses the points [tex]\((-4, -5)\)[/tex] and [tex]\((2, 4)\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's apply this formula step-by-step with our given points:
1. Identify the coordinates:
- [tex]\((x_1, y_1) = (-4, -5)\)[/tex]
- [tex]\((x_2, y_2) = (2, 4)\)[/tex]
2. Substitute these values into the slope formula:
[tex]\[ m = \frac{4 - (-5)}{2 - (-4)} \][/tex]
3. Simplify the numerator and the denominator:
- Numerator: [tex]\(4 - (-5) = 4 + 5 = 9\)[/tex]
- Denominator: [tex]\(2 - (-4) = 2 + 4 = 6\)[/tex]
4. Divide the simplified numbers:
[tex]\[ m = \frac{9}{6} \][/tex]
5. Reduce the fraction to its simplest form:
[tex]\[ \frac{9}{6} = \frac{3}{2} \][/tex]
Therefore, the slope of the line that crosses the points [tex]\((-4, -5)\)[/tex] and [tex]\((2, 4)\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].
To find the gradient (slope) we use the formula
(change in y)/(change in x)
Subbing in that gives us:
-5 - 4 / -4 - 2
Which is equal to:
-9 / -6 or 3/2
(change in y)/(change in x)
Subbing in that gives us:
-5 - 4 / -4 - 2
Which is equal to:
-9 / -6 or 3/2
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