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what is the slope of the line that passes through the points (4,4) and (10,7)? write your answer in simplest form

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Sarah06109

Answer:

[tex]\boxed {\boxed {\sf m= \frac{1}{2}}}[/tex]

Step-by-step explanation:

We are asked to find the slope of a line that passes through 2 points. The slope tells us the steepness and direction of a line. It is calculated using the following formula:

[tex]m= \frac {y_2-y_1}{x_2-x_1}[/tex]

In this formula, (x₁ , y₁) and (x₂, y₂) are the points the line passes through. The points are (4,4) and (10,7). If we match the value and the corresponding variable we see that:

  • x₁ = 4
  • y₁= 4
  • x₂ = 10
  • y₂= 7

Substitute the values into the formula.

[tex]m= \frac{7-4}{10-4}[/tex]

Solve the numerator.

  • 7-4=3

[tex]m= \frac{3}{10-4}[/tex]

Solve the denominator.

  • 10-4= 6

[tex]m= \frac{3}{6}[/tex]

This fraction can be reduced. Both the numerator and denominator can be divided by 3.

[tex]m= \frac{3/3}{6/3}[/tex]

[tex]m= \frac{1}{2}[/tex]

The slope of the line that passes through (4,4) and (10,7) is 1/2.

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