Algebra Examples

$y = 5 x - 3$

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 $x$ .

$0 = 5 x - 3$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $5 x - 3 = 0$ .

$5 x - 3 = 0$

Step 1.2.2

Add $3$ to both sides of the equation.

$5 x = 3$

Step 1.2.3

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

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Step 1.2.3.1

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

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

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $5$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

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

Step 1.2.3.2.1.2

Divide $x$ by $1$ .

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

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$y = 5 (0) - 3$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 5 (0) - 3$

Step 2.2.2

Simplify $5 (0) - 3$ .

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Step 2.2.2.1

Multiply $5$ by $0$ .

$y = 0 - 3$

Step 2.2.2.2

Subtract $3$ from $0$ .

$y = - 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 3)$

Step 4