y= mx+b
In this form, m is the slope of the line 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,-4). This means that the value of b is -4.
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. In doing so, we will be able to identify the slope m using the rise and run of the graph.
Here we've identified (3,-6) as our other point. Traveling to this point from the y-intercept requires that we move 3 steps horizontally in the positive direction and 2 steps vertically in the negative direction.
rise/run=-2/3 ⇔ m= -2/3
Writing the Equation
Now that we have the slope and the y-intercept, we can form our final equation.
y= mx+b
y= -2/3x+(-4) ⇒ y=-2/3x-4
b Let's take a look at the given graph.
We can see that the line is horizontal, so its slope is equal to 0. Since the graph passes point (1,2), the y-value of each point that lies on this line will be equal to 2.
y= mx+b
y= 0x+2 ⇒ y=2
c Again, first let's look carefully at the graph.
This time the line is vertical, which means its slope is undefined. By looking at the graph we can see that each point that has x-value equal to 2 lies on our line. With this, we can write the equation.
x= 2
d For the last time let's recall a format of equations written in slope-intercept form.
y= mx+b
Remember that in this form, m is the slope of the line and b is the y-intercept. To find the equation, first observe the given graph.
From the graph we are given two points that lies on the line. By substituting them into the Slope Formula we are able to find the slope m.
