Which of the following represents a linear equation in slope-intercept form?

Slope intercept form is commonly written as:

Where m is our slope and b is our intercept. Note that m and b can be negative.

Now, we are asked to find the equation which is in slope intercept form. This means, we want an option which looks like the above form.

First, rule out anything that isn't linear. Linear equation describe a straight line, whereas other equations may be curved.

Is a quadratic equation, so it is not our answer

Is not linear either, it is a reciprocal function.

Thus, we are left with:

Of these, only the second is in the correct form. The first could be rearranged to be in slope-intercept form, but it is not currently.

So, our answer is:

Start by rewriting the equation in slope-intercept form.

Recall that in the slope intercept form, ,  is the slope. For the given equation, . The slope must be .

To find the y-intercept, we must have our linear equation in slope-intercept form:

, where  represents the y-intercept

Our equation is already in this form:

Therefore, our y-intercept is 

The slope of the line is apparent when we have our equation in slope-intercept form

, where  is the slope

Put  into slope-intercept form

1)  (divide each piece by )

2) 

Therefore, as this equation corresponds with , we have our slope given as 

The slope-intercept form of a linear equation is represented as:

The choice that corresponds to this form is:

where  and 

Remember that the slopes of perpendicular lines are each other's negative reciprocal.

To find the negative reciprocal of a number, we put it into fraction form, invert the numerator and the denominator, and negate the result.

For example: 

  (invert the numerator and denominator)

  (negate the result)

In our example, the slope of our equation is 

  (invert the numerator and denominator)

  (negate the result)

Therefore, the slope of a line perpendicular to the line  is 

Parallel lines have identical slopes. The y-intercept, in this case, is irrelevant.

The line which has the same slope as  is:

In our equation , we need to find the slope, , and the y-intercept, .

To find the slope of a line given two points, , we have our slope formula:

So, given , we can find the slope by substituting those values into our slope formula:

Our y-intercept was given as , so, 

We have our  and our , so the answer is 

A linear equation in standard form is represented by: 

In our equation, , we can arrange these values to get it into its standard form:

 (add  to both sides)

Or, , which is in the form 

First, get the equation into slope-intercept form 

 (divide both sides by 6)

We can clearly see the y-intercept as 

For the slope, notice that there is an invisible coefficient of  in front of the . That is our slope.