Pre-Algebra Examples

$1.5 (y - 10) = 0.3 - y$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $1.5 (y - 10)$ .

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Step 1.2.1.1

Apply the distributive property.

$1.5 y + 1.5 \cdot - 10 = 0.3 - y$

Step 1.2.1.2

Multiply $1.5$ by $- 10$ .

$1.5 y - 15 = 0.3 - y$

Step 1.3

Move all terms containing $y$ to the left side of the equation.

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Step 1.3.1

Add $y$ to both sides of the equation.

$1.5 y - 15 + y = 0.3$

Step 1.3.2

Add $1.5 y$ and $y$ .

$2.5 y - 15 = 0.3$

Step 1.4

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

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Step 1.4.1

Add $15$ to both sides of the equation.

$2.5 y = 0.3 + 15$

Step 1.4.2

Add $0.3$ and $15$ .

$2.5 y = 15.3$

Step 1.5

Divide each term in $2.5 y = 15.3$ by $2.5$ and simplify.

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Step 1.5.1

Divide each term in $2.5 y = 15.3$ by $2.5$ .

$\frac{2.5 y}{2.5} = \frac{15.3}{2.5}$

Step 1.5.2

Simplify the left side.

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Step 1.5.2.1

Cancel the common factor of $2.5$ .

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Step 1.5.2.1.1

Cancel the common factor.

$\frac{2.5 y}{2.5} = \frac{15.3}{2.5}$

Step 1.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{15.3}{2.5}$

Step 1.5.3

Simplify the right side.

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Step 1.5.3.1

Divide $15.3$ by $2.5$ .

$y = 6.12$

Step 2

Using the slope-intercept form, the y-intercept is $6.12$ .

$b = 6.12$

Step 3

y-intercept in point form.

$(0, 6.12)$

Step 4