Question

The graph of a linear relationship has a y-intercept at (0, 4) and passes through the point (2, 5)
Create an equation that represents the linear relationship

Answer 1

To find the equation of the linear relationship, we can use the slope-intercept form of a linear equation, which is:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. We are given that the y-intercept is at (0, 4), so we have:

\[ b = 4 \]

Next, we need to find the slope \( m \). The slope is calculated using the two points we have: the y-intercept (0, 4) and the point (2, 5):

Using the formula for slope \( m \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let \( (x_1, y_1) = (0, 4) \) and \( (x_2, y_2) = (2, 5) \):

\[ m = \frac{5 - 4}{2 - 0} = \frac{1}{2} \]

Now we have both \( m \) and \( b \):

- Slope \( m = \frac{1}{2} \)
- Y-intercept \( b = 4 \)

Substituting these values into the slope-intercept form gives us:

\[ y = \frac{1}{2}x + 4 \]

Thus, the equation that represents the linear relationship is:

\[ y = \frac{1}{2}x + 4 \]