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An illustration shows a coordinate plane with four quadrants. The x and y axes extend from negative 10 to 10 in increments of 1. Two points are plotted on the graph. An upward slanting line connects the two points. Point A is plotted at coordinates left parenthesis 1 comma negative 2 right parenthesis. Point B is plotted at left parenthesis 6 comma 1 right parenthesis.

Determine the slope of the line.

(1 point)
Responses

−35
negative Start Fraction 3 over 5 End Fraction

35
Start Fraction 3 over 5 End Fraction

−53
negative Start Fraction 5 over 3 End Fraction

53
Start Fraction 5 over 3 End Fraction
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1 answer

To find the slope of the line connecting the two points \( A(1, -2) \) and \( B(6, 1) \), we can use the slope formula:

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

where \( (x_1, y_1) \) are the coordinates of point A and \( (x_2, y_2) \) are the coordinates of point B.

Here, we have:

  • \( x_1 = 1 \)
  • \( y_1 = -2 \)
  • \( x_2 = 6 \)
  • \( y_2 = 1 \)

Substituting these values into the formula:

\[ m = \frac{1 - (-2)}{6 - 1} = \frac{1 + 2}{5} = \frac{3}{5} \]

Thus, the slope of the line is:

\[ \frac{3}{5} \]

The correct response is:

Start Fraction 3 over 5 End Fraction.