Question

trazar la recta.
$y=\frac{1}{3}x + 5$

Explanation:

Step1: Identify the slope-intercept form

The equation \( y = \frac{1}{3}x + 5 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{1}{3} \) (slope) and \( b = 5 \) (y - intercept).

Step2: Plot the y - intercept

The y - intercept \( b = 5 \) means the line crosses the y - axis at the point \( (0,5) \). Locate the point \( (0,5) \) on the coordinate grid.

Step3: Use the slope to find another point

The slope \( m=\frac{1}{3}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,5) \), we can rise (move up) 1 unit and run (move right) 3 units. So we get the point \( (0 + 3,5+1)=(3,6) \). We can also go in the opposite direction: rise - 1 (move down) and run - 3 (move left) from \( (0,5) \) to get \( (0-3,5 - 1)=(-3,4) \).

Step4: Draw the line

Using a straight - edge, draw a line that passes through the points we found (e.g., \( (0,5) \), \( (3,6) \), \( (-3,4) \)). Extend the line in both directions to show it is a straight line.

Answer:

To graph the line \( y=\frac{1}{3}x + 5 \), plot the y - intercept at \( (0,5) \), use the slope \( \frac{1}{3} \) to find another point (e.g., \( (3,6) \) or \( (-3,4) \)), and then draw a straight line through these points.