Question

Write the equation of a line that passes through the point (-5,-4) and has a slope of 1/5

Answer 1

Linear Equations

Typically, linear equations are written in slope-intercept form:

`y=mx+b`

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

To find the equation of a line given a point and the slope:

1. Plug the slope into y=mx+b as m
2. Plug the point into y=mx+b as (x,y)
3. Solve for b
4. Plug b back into y=mx+b along with m

Solving the Question

We're given:

• 
  `m=(1)/(5)`
• Passes through (-5,-4)

`y=mx+b`

⇒ Plug in the slope,
`(1)/(5)`:

`y=(1)/(5)x+b`

⇒ Plug in the point (-5,-4) and solve for b:

`-4=(1)/(5)(-5)+b\\\\-4=-1+b\\\\b=-3`

⇒ Therefore, the y-intercept of the line is -3. Plug this back into our original equation as b:

`y=(1)/(5)x-3`

Answer

`y=(1)/(5)x-3`