Algebra Examples

What is the equation of the line that passes through the point $(5, 0)$ and has a slope of $- 1$ ?

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.

$y = (- 1) \cdot x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (- 1) \cdot (5) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$0 = (- 1) \cdot (5) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $(- 1) \cdot (5) + b = 0$ .

$(- 1) \cdot (5) + b = 0$

Step 1.5.2

Multiply $- 1$ by $5$ .

$- 5 + b = 0$

Step 1.5.3

Add $5$ to both sides of the equation.

$b = 5$

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.

$y = - x + 5$

Step 3