Find the Equation Using Slope-Intercept Form (10,0) , m=1/2

$(10, 0)$ , $m = \frac{1}{2}$

Step 1

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

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

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (\frac{1}{2}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{1}{2}) \cdot (10) + b$

Substitute the value of $y$ into the equation.

$0 = (\frac{1}{2}) \cdot (10) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{2} \cdot 10 + b = 0$ .

$\frac{1}{2} \cdot 10 + b = 0$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{1}{2} \cdot (2 (5)) + b = 0$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 5) + b = 0$

Rewrite the expression.

$5 + b = 0$

Subtract $5$ from 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.

$y = \frac{1}{2} x - 5$

Step 3