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 equation in standard form is:  

Simplify the right side by distribution.

Subtract  on both sides.

The equation becomes: 

Subtract 3 from both sides.

The answer is:  

We will first need to write the point-slope form to set up the equation.

Substitute the slope and point.

Simplify the right side.

Add 3 on both sides.

Subtract  on both sides.

The answer is:  

Distribute the right side.

Subtract  on both sides.

The answer is:  

The standard form of a linear equation is:  

Multiply by two on both sides to eliminate the fraction.

Subtract  on both sides.

Subtract 6 from both sides.

The answer is:  

The standard form of a line is:  

First, we can write the equation in slope-intercept form:  

Subtract  on both sides.

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:  

Distribute the four through both terms of the binomial.

Subtract  on both sides of the equation.

Simplify both sides.

The answer is:  

First, find the slope-intercept form of the equation. This is 

,

where  is the slope and  is the -intercept of the line. Since  is this intercept, . Also, the slope of a line with intercepts  and  is , so, setting ,

.

The slope-intercept form is 

The standard form of the equation is 

,

where, by custom, , , and  are relatively prime integers, and . To accomplish this:

Switch the expressions:

Add  to both sides:

Multiply both sides by 3 to eliminate the denominator and make the coefficients integers with GCF 1:

Distribute on the left:

This is 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.