Question

What is the equation of the line that has a slope of m = 2 and passes through the point (-5, -6)?

Answer 1

`y=2x+4`

Explanation:

You can solve this two ways: insert the values into point-slope form and simplify to solve for y, converting it to slope-intercept form, or insert the values into slope-intercept form, solve for b, and insert b. We'll do both :)

Point-slope form:

`y-y_(1)=m(x-x_(1))`

Where:

• 
  `m` is the slope

• 
  `x_(1)` and
  `y_(1)` are corresponding coordinate points
  `(x,y)`

Insert the given values:

`m=2\\\\(-5_{x_(1)},-6_{y_(1)})\\\\y-(-6)=2(x-(-5))\\\\y+6=2(x+5)`

Solve for y. Expand the right sie using the distributive property:

`y+6=2(x)+2(5)\\\\y+6=2x+10`

Isolate the variable. Subtract 6 from both sides, canceling out the 6 on the left:

`y+6-6=2x+10-6\\\\y=2x+4`

OR

Slope-intercept form:

`y=mx+b`

Where:

• 
  `m` is the slope
• 
  `b` is the y-intercept
• 
  `x` and
  `y` are corresponding coordinate points
  `(x,y)`

Insert the given values:

`m=2\\\\(-5_(x),-6_(y))\\\\-6=2(-5)+b`

Simplify the multiplication:

`-6=-10+b`

Solve for b. Add 10 to both sides, canceling out the 10 on the right:

`-6+10=-10+10+b\\\\4=b`

The value of b is 4. Insert the appropriate information into the equation. When using slope-intercept form, you don't plug in the coordinate points:

`y=2x+4`

:Done