Finite Math Examples

$4 x + 3 y = 21$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$4 x + 3 (0) = 21$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $4 x + 3 (0)$ .

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Step 1.2.1.1

Multiply $3$ by $0$ .

$4 x + 0 = 21$

Step 1.2.1.2

Add $4 x$ and $0$ .

$4 x = 21$

Step 1.2.2

Divide each term in $4 x = 21$ by $4$ and simplify.

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Step 1.2.2.1

Divide each term in $4 x = 21$ by $4$ .

$\frac{4 x}{4} = \frac{21}{4}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{21}{4}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{21}{4}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{21}{4}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$4 (0) + 3 y = 21$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $4 (0) + 3 y$ .

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Step 2.2.1.1

Multiply $4$ by $0$ .

$0 + 3 y = 21$

Step 2.2.1.2

Add $0$ and $3 y$ .

$3 y = 21$

Step 2.2.2

Divide each term in $3 y = 21$ by $3$ and simplify.

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Step 2.2.2.1

Divide each term in $3 y = 21$ by $3$ .

$\frac{3 y}{3} = \frac{21}{3}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{21}{3}$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{21}{3}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide $21$ by $3$ .

$y = 7$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

Step 3

List the intersections.

x-intercept(s): $(\frac{21}{4}, 0)$

y-intercept(s): $(0, 7)$

Step 4