Find the Equation with a Point and y-intercept (10,10) , b=1

$(10, 10)$ , $b = 1$

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

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = m x + 1$

Substitute the value of $x$ into the equation.

$y = m (10) + 1$

Substitute the value of $y$ into the equation.

$10 = m (10) + 1$

Find the value of $m$ .

Rewrite the equation as $m (10) + 1 = 10$ .

$m (10) + 1 = 10$

Move $10$ to the left of $m$ .

$10 m + 1 = 10$

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

Subtract $1$ from both sides of the equation.

$10 m = 10 - 1$

Subtract $1$ from $10$ .

$10 m = 9$

Divide each term in $10 m = 9$ by $10$ and simplify.

Divide each term in $10 m = 9$ by $10$ .

$\frac{10 m}{10} = \frac{9}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 m}{10} = \frac{9}{10}$

Divide $m$ by $1$ .

$m = \frac{9}{10}$

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.

$y = \frac{9}{10} x + 1$