Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

`y=(1)/(2)x +4`

Explanation:

Slope-intercept form is a common way of representing linear functions. Slope-intercept is written as y = mx + b, where m is the slope and b is the y-intercept.

Slope

To find the slope-intercept equation we first need to find the m-value. Slope is often defined as rise over run. This means the change in y divided by the change in x. So, we can find the slope by counting how much the y-value and the x-value increases between 2 points.

For example, we can take the points (2,5) and (4,6). The y-value increases by 1 and the x-values increase by 2. This means that the slope is 1/2. We can plug this into slope-intercept form to get part of the equation:
`y = (1)/(2)x+b`.

Y-Intercept

Next, we need to find the b-value. The y-intercept of a graph is the y-value where the function intersects with the y-axis (the vertical axis). By looking at the graph, we can tell that the function crosses the y-axis at y = 4; this occurs at the point (0,4). The y-intercept always occurs when x = 0.

Now, we can plug 4 in for b to get the final equation:
`y=(1)/(2)x +4`.