GRE Subject Test: Math : Finding Equations of Lines

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Finding Equations Of Lines

What is the equation of the line (in slope-intercept form) that goes through the points:  and ?

Possible Answers:

Correct answer:

Explanation:

Step 1: Find the slope between the two points:



Step 2: Write the slope-intercept form:



Step 3. Find b. Plug in (x,y) from one of the points:






Step 4: Write out the full equation:

Example Question #2 : Finding Equations Of Lines

What is the equation of a line that passes through points  and  in slope-intercept form?

Possible Answers:

Correct answer:

Explanation:

To find the equation of the line, first find the slope using the formula:

The points that the line passes through are  and .

Then pick one set of points and place in the form   . Either set of points will give you the same equation.  Points  were used.

Subtract    from both sides of the equation.

The equation of the line in slope-intercept form or    is

 

Example Question #3 : Finding Equations Of Lines

Find the equation of a line in slope-intercept form that passes though points  and .

Possible Answers:

Correct answer:

Explanation:

To find the equation of a line that passes through  and , first find the slope using this formula:

Using one set of points or coordinates and the value of slope, plug these values into:

Either set of points will give you the same equation of the line.

Coordinates .

Distribute the  to what is inside the parenthesis.

Add  to both sides of the equation.

The equation of the line in slope-intercept form    is:

Example Question #4 : Finding Equations Of Lines

A line has a slope of  and goes through point   What is the equation of the line in slope-intercept form?

Possible Answers:

Correct answer:

Explanation:

The slope-intercept form is , where  represents the slope,  and  represent the points, and  is the y-intercept or the value of  when 

The slope or  has been given as .

The points that this equation of the line passes through are  and

 because based on the points, when   That is the y-intercept.

The equation of the line in slope-intercept form  is:

Example Question #5 : Finding Equations Of Lines

Find the equation of a line in slope-intercept form that passes through points  and has a slope of 

Possible Answers:

Correct answer:

Explanation:

To find the equation of a line given points  and  use the point- slope formula:

Distribute the  to what is inside the parenthesis.

Subtract  from both sides of the equation.

  When the sign is the same for both integers, add.

The equation of the line in slope-intercept form    is:

Example Question #6 : Finding Equations Of Lines

Find the equation of the line with points 

Possible Answers:

Correct answer:

Explanation:

To solve for  you must use the equation 

To solve for be we must plug in one of the points

simplify

Add  to both sides

Example Question #7 : Finding Equations Of Lines

Find a line through the point  perpendicular to the line .

Possible Answers:

Correct answer:

Explanation:

To solve this problem you must first find the slope of the original equation by point it into y-mx+b form

subtract x from both sides

Then you must find the reciprocal of the slope to get the slope of the perpendicular line

 reciprocal is 

Finally you must you point-slope form to solve 

Multiply  through the parentheses

add three to both sides

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