Linear Equations
Linear equations are usually organized in slope-intercept form, which looks like this:
[tex]y=mx+b[/tex]
- m is the slope of the line
- b is the y-intercept (the value of y when the line passes through the y-axis)
To find the equation of a line in slope-intercept form:
- Determine the slope of the line
- Plug the slope into the general form
- Determine the y-intercept by solving for b
- Plug b back into the equation
Solving the Question
We're given:
- m = [tex]\dfrac{1}{2}[/tex]
- (4,1) falls on the line
First, plug the given slope into the slope-intercept form equation:
[tex]y=mx+b\\\\y=\dfrac{1}{2}x+b[/tex]
Now, determine the y-intercept.
[tex]y=\dfrac{1}{2}x+b[/tex]
⇒ Plug in the given point (4,1) and solve for b:
[tex]1=\dfrac{1}{2}(4)+b\\1=2+b\\b=-1[/tex]
⇒ Therefore, the y-intercept is -1. Plug this back into our original equation:
[tex]y=\dfrac{1}{2}x-1[/tex]
Answer
[tex]y=\dfrac{1}{2}x-1[/tex]
