Equations in slope-intercept form follow a certain format.
y= mx+ b
In this form, the coefficient m is the slope and the constant b is the y-intercept. We are told that the line has a slope of 3, which means that we can substitute m= 3.
y= 3x+ b
To write a complete equation for this line, we also need to determine the y-intercept b. We can do that by substituting the given point ( 3, -3) into the equation and solving for b.
Now that we have both the slope and the y-intercept, we can write the final equation.
y= 3x+( - 12) ⇔ y= 3x - 12
Let's take a look at the graph of this line by showing it on a coordinate plane.
Alternative Solution
Using Point-Slope Form
There is another form of linear equations called point-slope form.
y-y_1=m(x-x_1)
In this form, m is still the slope of the line and (x_1,y_1) is a point that lies on the line. With the given information, it is a much quicker process to write the equation of the line using point-slope form. Let's try!
