Question

step 2: \\(x_2 = 6\\) \\(y_2 = 3\\)

step 3: apply the slope formula: \\(m = \frac{y_2 - y_1}{x_2 - x_1}\\)
\\(m = \frac{3 - 2}{6 - (-1)} = (1/7)\\)

step 4: use one of the given points to find the \\(y\\)-intercept by substituting values for \\(x\\), \\(y\\), and \\(m\\) into the equation \\(y = mx + b\\).
for example, if \\(x = -1\\) and \\(y = 2\\), solve the equation \\(2 = \frac{1}{7}(-1) + b\\)
\\(b = \\)

Explanation:

Identify the given equation

Using the Variable Substitution knowledge point

$$ 2 = \frac{1}{7}(-1) + b $$

Simplify the multiplication

Using the Algebraic Rearrangement knowledge point

$$ 2 = -\frac{1}{7} + b $$

Isolate the variable b

Using the Algebraic Rearrangement knowledge point

$$ b = 2 + \frac{1}{7} $$

Calculate the final value

Using the Algebraic Rearrangement knowledge point

$$ b = \frac{14}{7} + \frac{1}{7} = \frac{15}{7} $$

Answer:

For example, if \(x = -1\) and \(y = 2\), solve the equation \(2 = \frac{1}{7}(-1) + b\): \(b =\) <blank>\(\frac{15}{7}\)</blank>