Question

select the correct answer from each drop-down menu.

the slope of the line passing through the points \\((7, 5)\\) and \\((21, 15)\\) is choose an answer.
another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point choose an answer.

Explanation:

Calculate the slope of the first line

Using the Slope of a Line knowledge point

$$ m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{15 - 5}{21 - 7} = \frac{10}{14} = \frac{5}{7} $$

Determine the slope of the second line

Using the Linear Equations knowledge point

$$ m_2 = \frac{1}{3} \cdot m_1 = \frac{1}{3} \cdot \frac{5}{7} = \frac{5}{21} $$

Identify the point on the second line

The second line passes through the origin \((0,0)\) and has a slope of \(\frac{5}{21}\).
Its equation is:

$$ y = \frac{5}{21}x $$

Any point \((x, y)\) on this line must satisfy this proportional relationship. A natural integer coordinate point on this line is \((21, 5)\).

Answer:

Select the correct answer from each drop-down menu.

The slope of the line passing through the points (7, 5) and (21, 15) is <blank>\(\frac{5}{7}\)</blank>.
Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point <blank>\((21, 5)\)</blank>.