Question

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

Answer 1

Answer:

$y=2x+4$

Step-by-step 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