Find the Constant Using Slope

$2 y = k x + 4$ , $m = 2$

Step 1

Divide each term in $2 y = k x + 4$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 y = k x + 4$ by $2$ .

$\frac{2 y}{2} = \frac{k x}{2} + \frac{4}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{k x}{2} + \frac{4}{2}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{k x}{2} + \frac{4}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $4$ by $2$ .

$y = \frac{k x}{2} + 2$

Step 2

Find the slope of the equation in terms of $k$ using the slope-intercept form.

$m = \frac{k}{2}$

Step 3

Set the known value of $m$ equal to the slope of the equation in terms of $k$ .

$2 = \frac{k}{2}$

Step 4

Rewrite the equation as $\frac{k}{2} = 2$ .

$\frac{k}{2} = 2$

Step 5

Multiply both sides of the equation by $2$ .

$2 \frac{k}{2} = 2 \cdot 2$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

$2 \frac{k}{2} = 2 \cdot 2$

Step 6.1.1.2

Rewrite the expression.

$k = 2 \cdot 2$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $2$ by $2$ .

$k = 4$

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