Algebra Examples

What is the equation of the line that passes through the point $(- 7, - 7)$ and has a slope of $1$ ?

Step 1

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

Tap for more steps...

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.

$y = (1) \cdot (- 7) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$- 7 = (1) \cdot (- 7) + b$

Step 1.5

Find the value of $b$ .

Tap for more steps...

Step 1.5.1

Rewrite the equation as $(1) \cdot (- 7) + b = - 7$ .

$(1) \cdot (- 7) + b = - 7$

Step 1.5.2

Multiply $- 7$ by $1$ .

$- 7 + b = - 7$

Step 1.5.3

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

Tap for more steps...

Step 1.5.3.1

Add $7$ to both sides of the equation.

$b = - 7 + 7$

Step 1.5.3.2

Add $- 7$ and $7$ .

$b = 0$

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.

$y = x$

Step 3