Algebra Examples

$y - 1 = \frac{3}{5} x - \frac{3}{5} \cdot 5$

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 $x$ .

$(0) - 1 = \frac{3}{5} x - \frac{3}{5} \cdot 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{3}{5} x - \frac{3}{5} \cdot 5 = (0) - 1$ .

$\frac{3}{5} x - \frac{3}{5} \cdot 5 = (0) - 1$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

Combine $\frac{3}{5}$ and $x$ .

$\frac{3 x}{5} - \frac{3}{5} \cdot 5 = (0) - 1$

Step 1.2.2.2

Cancel the common factor of $5$ .

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Step 1.2.2.2.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{3 x}{5} + \frac{- 3}{5} \cdot 5 = (0) - 1$

Step 1.2.2.2.2

Cancel the common factor.

$\frac{3 x}{5} + \frac{- 3}{5} \cdot 5 = (0) - 1$

Step 1.2.2.2.3

Rewrite the expression.

$\frac{3 x}{5} - 3 = (0) - 1$

Step 1.2.3

Subtract $1$ from $0$ .

$\frac{3 x}{5} - 3 = - 1$

Step 1.2.4

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.4.1

Add $3$ to both sides of the equation.

$\frac{3 x}{5} = - 1 + 3$

Step 1.2.4.2

Add $- 1$ and $3$ .

$\frac{3 x}{5} = 2$

Step 1.2.5

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} \cdot \frac{3 x}{5} = \frac{5}{3} \cdot 2$

Step 1.2.6

Simplify both sides of the equation.

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Step 1.2.6.1

Simplify the left side.

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Step 1.2.6.1.1

Simplify $\frac{5}{3} \cdot \frac{3 x}{5}$ .

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Step 1.2.6.1.1.1

Cancel the common factor of $5$ .

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Step 1.2.6.1.1.1.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 x}{5} = \frac{5}{3} \cdot 2$

Step 1.2.6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{5}{3} \cdot 2$

Step 1.2.6.1.1.2

Cancel the common factor of $3$ .

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Step 1.2.6.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{5}{3} \cdot 2$

Step 1.2.6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{5}{3} \cdot 2$

Step 1.2.6.1.1.2.3

Rewrite the expression.

$x = \frac{5}{3} \cdot 2$

Step 1.2.6.2

Simplify the right side.

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Step 1.2.6.2.1

Multiply $\frac{5}{3} \cdot 2$ .

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Step 1.2.6.2.1.1

Combine $\frac{5}{3}$ and $2$ .

$x = \frac{5 \cdot 2}{3}$

Step 1.2.6.2.1.2

Multiply $5$ by $2$ .

$x = \frac{10}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{10}{3}, 0)$

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 $y$ .

$y - 1 = \frac{3}{5} \cdot (0) - \frac{3}{5} \cdot 5$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $\frac{3}{5} \cdot (0) - \frac{3}{5} \cdot 5$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Multiply $\frac{3}{5}$ by $0$ .

$y - 1 = 0 - \frac{3}{5} \cdot 5$

Step 2.2.1.1.2

Cancel the common factor of $5$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$y - 1 = 0 + \frac{- 3}{5} \cdot 5$

Step 2.2.1.1.2.2

Cancel the common factor.

$y - 1 = 0 + \frac{- 3}{5} \cdot 5$

Step 2.2.1.1.2.3

Rewrite the expression.

$y - 1 = 0 - 3$

Step 2.2.1.2

Subtract $3$ from $0$ .

$y - 1 = - 3$

Step 2.2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.2.1

Add $1$ to both sides of the equation.

$y = - 3 + 1$

Step 2.2.2.2

Add $- 3$ and $1$ .

$y = - 2$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

Step 3

List the intersections.

x-intercept(s): $(\frac{10}{3}, 0)$

y-intercept(s): $(0, - 2)$

Step 4