Equations in point-slope form follow a specific format.
y- y_1= m(x- x_1)
In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. Here we are given that the line passes through known points.
x
1
2
3
y
- 3
1
5
To determine the slope of the line, we can calculate the slope by substituting only two points of the given table into the Slope Formula.
Now that we know the slope of the line is 4, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 2, 1).
y-y_1=m(x-x_1)
⇕
y- 1= 4(x- 2)
Since any point on the line could be used to form a point-slope equation, there are infinitely many possible equations. To write a unique equation for this line, we will rewrite it in slope-intercept form.
Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!
