Question

comparing functions: mastery test

\\(y = \frac{7}{5}x + \frac{2}{3}\\)
\\(y = \frac{7}{5}x + \frac{7}{5}\\)
\\(y = \frac{6}{5}x + \frac{11}{5}\\)
\\(y = \frac{5}{4}x + \frac{15}{4}\\)

Explanation:

Identify points on the line

$$ (x_1, y_1) = (2, 1),\quad (x_2, y_2) = (7, 7) $$

Calculate the slope

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 1}{7 - 2} = \frac{6}{5} $$

Determine the equation in slope-intercept form

$$
LATEXBLOCK0
$$

Answer:

• (A) \(y = \frac{7}{5}x + \frac{2}{3}\)
• (B) \(y = \frac{7}{5}x + \frac{7}{5}\) (Correct answer)
• (C) \(y = \frac{6}{5}x + \frac{11}{5}\)
• (D) \(y = \frac{5}{4}x + \frac{15}{4}\)