Question

What is the equation of the line that passes through the point (4,1) and has a slope
of 1/2

Answer 1

Linear Equations

Linear equations are usually organized in slope-intercept form, which looks like this:

$y=mx+b$

• 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:

1. Determine the slope of the line
2. Plug the slope into the general form
3. Determine the y-intercept by solving for b
4. Plug b back into the equation

Solving the Question

We're given:

• m = $\dfrac{1}{2}$
• (4,1) falls on the line

First, plug the given slope into the slope-intercept form equation:

$y=mx+b\\\\y=\dfrac{1}{2}x+b$

Now, determine the y-intercept.

$y=\dfrac{1}{2}x+b$

⇒ Plug in the given point (4,1) and solve for b:

$1=\dfrac{1}{2}(4)+b\\1=2+b\\b=-1$

⇒ Therefore, the y-intercept is -1. Plug this back into our original equation:

$y=\dfrac{1}{2}x-1$

Answer

$y=\dfrac{1}{2}x-1$