Question

6 encuentra la pendiente de la recta ( y = \frac{1}{6}x + \frac{9}{2} ). la intersección con el eje y es

Explanation:

To solve for the \( y \)-intercept of the line \( y = \frac{1}{6}x + \frac{9}{2} \), we use the slope - intercept form of a linear equation \( y=mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. The \( y \)-intercept is the value of \( y \) when \( x = 0 \).

Step 1: Recall the slope - intercept form

The equation of a line in slope - intercept form is given by \( y=mx + b \), where:

• \( m \) represents the slope of the line.
• \( b \) represents the \( y \)-coordinate of the point where the line intersects the \( y \)-axis (i.e., when \( x = 0 \)).

Step 2: Identify the \( y \)-intercept from the given equation

We are given the equation \( y=\frac{1}{6}x+\frac{9}{2} \). Comparing this equation with the slope - intercept form \( y = mx + b \):

• The slope \( m=\frac{1}{6} \).
• The \( y \)-intercept \( b=\frac{9}{2} \). We can also verify this by substituting \( x = 0 \) into the equation:

When \( x = 0 \), we have \( y=\frac{1}{6}(0)+\frac{9}{2}\). Since \(\frac{1}{6}(0) = 0\), then \( y=\frac{9}{2}\). So the line intersects the \( y \)-axis at the point \((0,\frac{9}{2})\), and the \( y \)-intercept is \(\frac{9}{2}\).

Step 3: Find the slope

From the slope - intercept form \( y=mx + b \) of the line \( y=\frac{1}{6}x+\frac{9}{2} \), the coefficient of \( x \) is the slope. So the slope \( m=\frac{1}{6}\).

For the slope:

Answer:

\(\frac{1}{6}\)

For the \( y \)-intercept: