Standard Form

First, we need to find the slope of the above line.

Given two points, , the slope can be calculated using the following formula:

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set and :

Since we are looking for standard form - that is, - we do the following:

or

The standard form of a linear equation is:

Reorganize the terms.

Add on both sides.

Subtract on both sides.

Subtract four on both sides.

The answer is:

The standard form of a line is , where are integers.

We therefore need to rewrite so it looks like .

The steps to do this are below:

The standard form of a line is , where all constants are integers, i.e. whole numbers.

Therefore, the equation written in standard form is .

To rewrite in standard form, we will need the equation in the form of:

Subtract on both sides.

Regroup the variables on the left, and simplify the right.

The answer is:

The standard form of a line is:

We can use the point-slope form of a line since we are only given the slope and a point.

Substitute the slope and the point.

Simplify this equation.

Add on both sides.

Subtract from both sides.

Simplify both sides.

The answer is:

Start by writing out the equation of the line in point-slope form.

Simplify this equation.

Now, recall what the standard form of a linear equation looks like:

, where are integers. Traditionally, is positive.

Rearrange the equation found from the point-slope form so that it has the and terms on one side, and a number on the other side.

Since the term should be positive, multiply the entire equation by .

Write the slope-intercept form of a linear equation.

Substitute the point and the slope.

Solve for the y-intercept, and then write the equation of the line.

The equation in standard form is:

Subtract from both sides.

The answer is:

The -intercept of the line can be seen to be at the point five units above the origin, which is . The -intercept is at the point three units to the right of the origin, which is . From these intercepts, we can find slope by setting in the formula

The slope is

Now, we can find the slope-intercept form of the line

By setting , :

The standard form of a linear equation in two variables is

,

so in order to find the equation in this form, first, add to both sides:

We can eliminate the fraction by multiplying both sides by 3:

Distribute by multiplying:

,

the correct equation.

The standard form of the equation of a line is

.

To rewrite the equation

in this form so that has a positive coefficient, first, switch the places of the expressions:

Get the term on the left and the constant on the right by adding to both sides:

To eliminate fractions and ensure that the coefficients are relatively prime, multiply both sides by lowest common denominator 14:

Multiply 14 by both expressions in the parentheses:

Cross-canceling:

,

the correct choice.