Identify the y-intercept and use the other point that is given on the grid.
y=5x-2
Practice makes perfect
Equations written in slope-intercept form follow a specific format.
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
Let's look at 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, 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 used the given (1,3) as our other point. Traveling to this point from the y-intercept requires that we move 1 step horizontally in the positive direction and 5 steps vertically in the positive direction.
rise/run=5/1 ⇔ m= 5
Writing the Equation
Now that we know the slope and the y-intercept, we can form our final equation.
y= mx+ b
⇓
y= 5x+( -2)
Therefore, the equation of the line for the given graph is y=5x-2.
