Question

sketch the graph of \\(y = \frac{5x}{3} + 7\\)

Explanation:

Identify the y-intercept

The equation is given in slope-intercept form:

$$y = \frac{5}{3}x + 7$$

The y-intercept is \( (0, 7) \).

Determine the slope

The slope of the line is:

$$m = \frac{5}{3}$$

Since the slope is positive, the line rises from left to right.

Find the x-intercept

Set \( y = 0 \) to find the x-intercept:

$$0 = \frac{5}{3}x + 7$$

$$\frac{5}{3}x = -7$$

$$x = -\frac{21}{5} = -4.2$$

The x-intercept is \( (-4.2, 0) \).

Match with the options

• Option 1: The y-intercept is at \( (0, -7) \). This is incorrect.
• Option 2: The y-intercept is at \( (0, 7) \) and the x-intercept is at approximately \( (-4.2, 0) \). This is correct.
• Option 3: The line has a negative slope. This is incorrect.
• Option 4: The line has a negative slope. This is incorrect.

Answer:

• (A) Line with y-intercept at (0, -7)
• (B) Line with y-intercept at (0, 7) and x-intercept at (-4.2, 0) (Correct answer)
• (C) Line with negative slope and y-intercept at (0, 7)
• (D) Line with negative slope and y-intercept at (0, -5)