Algebra Examples

What is the equation of the line that passes through the point $(8, - 8)$ and has a slope of $- 2$ ?

Step 1

Find the value of $b$ using the formula for the equation of a line.

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Step 1.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 1.2

Substitute the value of $m$ into the equation.

$y = (- 2) \cdot x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (- 2) \cdot (8) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$- 8 = (- 2) \cdot (8) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $(- 2) \cdot (8) + b = - 8$ .

$(- 2) \cdot (8) + b = - 8$

Step 1.5.2

Multiply $- 2$ by $8$ .

$- 16 + b = - 8$

Step 1.5.3

Move all terms not containing $b$ to the right side of the equation.

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Step 1.5.3.1

Add $16$ to both sides of the equation.

$b = - 8 + 16$

Step 1.5.3.2

Add $- 8$ and $16$ .

$b = 8$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - 2 x + 8$

Step 3