Identify the y-intercept. Then, find another point that lies on the grid.
y=-1/3x-2
Practice makes perfect
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. Let's start with the y-intercept.
Finding the y-intercept
Observe the given graph.
We can see that the function intercepts the y-axis at (0, -2). This means that the value of b is -2.
Finding the 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. Doing so, we will be able to identify the slope m using the rise and run of the graph.
Here we have identified (3,-3) as our other point. Traveling to this point from the y-intercept requires that we move 3 steps horizontally in the positive direction and 1 step vertically in the negative direction.
rise/run=-1/3 ⇔ m= -1/3
Writing the Equation
Now that we have the slope and the y-intercept, we can form our final equation.
y= mx+ b
y= -1/3x+( -2) ⇒ y=-1/3x-2
