Precalculus Examples

$3 x + 2 y = 5$

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 $x$ .

$3 x + 2 (0) = 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $3 x + 2 (0)$ .

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Step 1.2.1.1

Multiply $2$ by $0$ .

$3 x + 0 = 5$

Step 1.2.1.2

Add $3 x$ and $0$ .

$3 x = 5$

Step 1.2.2

Divide each term in $3 x = 5$ by $3$ and simplify.

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Step 1.2.2.1

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{3}, 0)$

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 $y$ .

$3 (0) + 2 y = 5$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $3 (0) + 2 y$ .

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Step 2.2.1.1

Multiply $3$ by $0$ .

$0 + 2 y = 5$

Step 2.2.1.2

Add $0$ and $2 y$ .

$2 y = 5$

Step 2.2.2

Divide each term in $2 y = 5$ by $2$ and simplify.

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Step 2.2.2.1

Divide each term in $2 y = 5$ by $2$ .

$\frac{2 y}{2} = \frac{5}{2}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{5}{2}$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{2}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{5}{2})$

Step 3

List the intersections.

x-intercept(s): $(\frac{5}{3}, 0)$

y-intercept(s): $(0, \frac{5}{2})$

Step 4