Question

post test: linear equations

\\(\frac{5}{9}\\)

\\(\frac{5}{7}\\)

\\(\frac{7}{5}\\)

\\(\frac{9}{7}\\)

Explanation:

Identify points on the line

To find the slope of the line, we need to identify two points where the line crosses the grid intersections perfectly. Looking at the graph:

• The line passes through the origin, which is the point \((0, 0)\).
• Following the line to the right, it passes exactly through the grid intersection at \((7, 5)\).

Apply the slope formula

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the ratio of the vertical change (rise) to the horizontal change (run):

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Calculate the slope value

Substitute the identified points \((0, 0)\) and \((7, 5)\) into the formula:

$$m = \frac{5 - 0}{7 - 0} = \frac{5}{7}$$

Match with the given options

The calculated slope is \(\frac{5}{7}\). Let's compare this with the multiple-choice options:

• First option: \(\frac{5}{9}\)
• Second option: \(\frac{5}{7}\)
• Third option: \(\frac{7}{5}\)
• Fourth option: \(\frac{9}{7}\)

The correct option is the second one.

Answer:

• (A) \(\frac{5}{9}\)
• (B) \(\frac{5}{7}\) (Correct answer)
• (C) \(\frac{7}{5}\)
• (D) \(\frac{9}{7}\)