Question

slope
for 1 through 6 use the graphs to find the slope of the lines. always simplify the ratios.
1
2
m=-2
3
4
5
6
for numbers 7 – 18 use the slope formula (m = \\(\frac{y_2 - y_1}{x_2 - x_1}\\)) to calculate the slope of the ordered pairs for the lines. show your work and simplify if necessary.
7 (2, 1); (5, 3)
8 (8, 3); (2, 5)
9 (1, -4); (6, -2)
10 (-3, 1); (-7, 4)

Explanation:

Step1: Identify values for slope formula

For the points \((2, 1)\) (so \(x_1 = 2\), \(y_1 = 1\)) and \((5, 3)\) (so \(x_2 = 5\), \(y_2 = 3\)). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Substitute values into formula

Substitute \(y_2 = 3\), \(y_1 = 1\), \(x_2 = 5\), \(x_1 = 2\) into the formula: \(m=\frac{3 - 1}{5 - 2}\).

Step3: Simplify the fraction

Simplify numerator and denominator: \(3 - 1 = 2\), \(5 - 2 = 3\), so \(m=\frac{2}{3}\).

Answer:

\(\frac{2}{3}\)