We want to find the slope and the y-intercept of the graph of the given equation. To do it, let's recall the slope-intercept form of a linear equation.
Slope-Intercept Form of a Linear Equation
The slope-intercept form of a linear equation of a nonvertical line is y= mx + b. In this equation m is is the slope and y is the y -intercept.
Now, let's take a look at the given equation. We can see that it is already given in the slope-intercept form. We will highlight the slope m and the y -intercept b.
y= 3x+ 1
Looking at the given equation, we can see that the slope is 3 and the y-intercept is 1.
Extra
Graphing a Linear Equation
In this exercise we have found the slope and the y -intercept of the graph of the given equation. Let's see how the graph looks like. The first step when graphing a linear equation is to plot the y -intercept on a coordinate plane. In this case, the y -intercept is 1, so we plot a point at (0,1).
The second step is to use the slope to plot another point. In this case the slope is 3, so we move up 3 units and right 1 unit.
Finally, we draw a line through these two points. This is the graph of the given equation y=3x+1.
