We want to determine which student is correct. To do so, we will write an equation for the line in slope-intercept form. Then we will compare our equation with the equations obtained by Chrissie and George. Let's start by recalling that equations written in slope-intercept form follow a specific format.
y= mx+ b
In this form m is the slope and b is the y-intercept. We need to identify these values using the graph.
y-intercept
The y-intercept is the y-value where the line crosses the y-axis.
We can see that the function intercepts the y-axis at (0, 5). This means that the value of b is 5.
y= mx+ 5
Slope
To find the slope we will trace along the line on the given graph until we find a lattice point, which is a point that lies perfectly on the grid lines. By doing so we can identify the slope m using the rise and run of the graph.
Here we have identified (2,4) as our other point. Traveling from the y-intercept to this point requires that we move 2 steps horizontally in the positive direction and 1 step vertically in the negative direction.
Rise/Run=- 1/2 ⇔ m= - 1/2
Writing the Equation
Now that we have the slope m= - 12 and the y-intercept b= 5, we can write our final equation.
