Math  /  Algebra

Question1) Find the slope of the line that passes through the following two points: (1,3)3(5,5)(-1,3) \quad 3(5,5)

Studdy Solution

STEP 1

1. The problem requires finding the slope of a line given two points.
2. The slope of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated using the formula: $ m = \frac{y_2 - y_1}{x_2 - x_1} \]
3. The points given are \((-1, 3)\) and \((5, 5)\).

STEP 2

1. Identify the coordinates of the two points.
2. Apply the slope formula.
3. Simplify the expression to find the slope.

STEP 3

Identify the coordinates of the two points: - The first point is (1,3)(-1, 3), so x1=1x_1 = -1 and y1=3y_1 = 3. - The second point is (5,5)(5, 5), so x2=5x_2 = 5 and y2=5y_2 = 5.

STEP 4

Apply the slope formula: m=y2y1x2x1=535(1)m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{5 - (-1)}

STEP 5

Simplify the expression: m=25+1=26=13m = \frac{2}{5 + 1} = \frac{2}{6} = \frac{1}{3}

STEP 6

The slope of the line that passes through the points (1,3)(-1, 3) and (5,5)(5, 5) is: 13\boxed{\frac{1}{3}}

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