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

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:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Where:

[tex]m[/tex] is the slope

[tex]x_{1}[/tex] and [tex]y_{1}[/tex] are corresponding coordinate points [tex](x,y)[/tex]

Insert the given values:

[tex]m=2\\\\(-5_{x_{1}},-6_{y_{1}})\\\\y-(-6)=2(x-(-5))\\\\y+6=2(x+5)[/tex]

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

[tex]y+6=2(x)+2(5)\\\\y+6=2x+10[/tex]

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

[tex]y+6-6=2x+10-6\\\\y=2x+4[/tex]

OR

Slope-intercept form:

[tex]y=mx+b[/tex]

Where:

[tex]m[/tex] is the slope
[tex]b[/tex] is the y-intercept
[tex]x[/tex] and [tex]y[/tex] are corresponding coordinate points [tex](x,y)[/tex]

Insert the given values:

[tex]m=2\\\\(-5_{x},-6_{y})\\\\-6=2(-5)+b[/tex]

Simplify the multiplication:

[tex]-6=-10+b[/tex]

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

[tex]-6+10=-10+10+b\\\\4=b[/tex]

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:

[tex]y=2x+4[/tex]

:Done