Slope Equation rise

Question

m
run
What is the slope of this line?
У2 -У1
Х2 = X1
10'
-10
(2,0)
(0, -1)
10
-10-
slope =
• Answer
What is the equation of this line? choose your answer...
:: -1
2
:: 1
::1/2

Answer 1

To find the slope of the line using the points given, we can use the formula for slope \( m \):

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

Given the points \( (2, 0) \) and \( (0, -1) \):

• \( (x_1, y_1) = (0, -1) \)
• \( (x_2, y_2) = (2, 0) \)

Plugging these values into the slope formula:

\[ m = \frac{0 - (-1)}{2 - 0} = \frac{0 + 1}{2 - 0} = \frac{1}{2} \]

So, the slope of the line is:

Slope = \( \frac{1}{2} \)

Now, for the equation of the line, we can use the point-slope form of the line equation:

\[ y - y_1 = m(x - x_1) \]

Using one of the points, let's use \( (0, -1) \):

\[ y - (-1) = \frac{1}{2}(x - 0) \]

This simplifies to:

\[ y + 1 = \frac{1}{2}x \]

Subtracting 1 from both sides gives us:

\[ y = \frac{1}{2}x - 1 \]

So the equation of the line is \( y = \frac{1}{2}x - 1 \).

Final Answers:

• Slope = \( \frac{1}{2} \)
• Equation of the line: \( y = \frac{1}{2}x - 1 \)