Question

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what is the slope of the line that passes through the points (-2, -4) and (3, -9)? write your answer in simplest form.
answer attempt 1 out of 2
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Explanation:

To find the slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Step 1: Identify the coordinates of the two points

We are given the points \((-2,-4)\) and \((3,-9)\). So, \(x_1=-2\), \(y_1 = - 4\), \(x_2=3\) and \(y_2=-9\)

Step 2: Substitute the values into the slope formula

Substitute the values of \(x_1,y_1,x_2,y_2\) into the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

\(m=\frac{-9-(-4)}{3 - (-2)}\)

Step 3: Simplify the numerator and the denominator

Simplify the numerator: \(-9-(-4)=-9 + 4=-5\)

Simplify the denominator: \(3-(-2)=3 + 2 = 5\)

Step 4: Calculate the slope

Now we have \(m=\frac{-5}{5}=- 1\)

Final Answer

The slope of the line is \(\boxed{-1}\)

Answer:

To find the slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Step 1: Identify the coordinates of the two points

We are given the points \((-2,-4)\) and \((3,-9)\). So, \(x_1=-2\), \(y_1 = - 4\), \(x_2=3\) and \(y_2=-9\)

Step 2: Substitute the values into the slope formula

Substitute the values of \(x_1,y_1,x_2,y_2\) into the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

\(m=\frac{-9-(-4)}{3 - (-2)}\)

Step 3: Simplify the numerator and the denominator

Simplify the numerator: \(-9-(-4)=-9 + 4=-5\)

Simplify the denominator: \(3-(-2)=3 + 2 = 5\)

Step 4: Calculate the slope

Now we have \(m=\frac{-5}{5}=- 1\)

Final Answer

The slope of the line is \(\boxed{-1}\)