Question

What is the equation of the line that passes through the point (3, 5) and has a slope
of -1/3

Answer 1

Linear Equations

Linear equations are typically organized in slope-intercept form:

$y=mx+b$

• m = slope
• b = y-intercept (the value of y when the line crosses the y-axis)

To determine the equation of a line:

1. Find the slope
2. Plug the slope into y=mx+b
3. Plug in a point that falls on the line as (x,y)
4. Solve for b

Solving the Question

We're given:

• $m=-\dfrac{1}{3}$
• The lines passes through the point (3,5)

$y=mx+b$

⇒ Plug the slope into the equation:

$y=-\dfrac{1}{3}x+b$

⇒ Plug in the given point (3,5) and determine the y-intercept:

$5=-\dfrac{1}{3}(3)+b\\\\5=-1+b\\\\b=6$

⇒ Plug this back into the equation along with the slope:

$y=-\dfrac{1}{3}x+6$

Answer

$y=-\dfrac{1}{3}x+6$