What is the equation of a line given one point and another unknown value?

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In summary, a student had a SAT level geometry question and needed help solving for the slope. They redrew the picture and asked for assistance, but also wanted to learn how to solve it. The equation of a line was given, and the student was advised to find another equation in order to solve for the constants a and b.
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mynameisfunk
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Had a SAT level geometry question from a student and didn't know how to solve it. I redrew what the picture was and the question asked for the slope. I know PF better than that but don't just give me the answer bc I need to know how to solve.
 

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  • #2
There is not enough information on the picture. You need to specify the coordinates of two points to get the slope.
 
  • #3
Perhaps we're given that the point of intersection bisects the line segment between the axes. That would be solvable. OP, is that an additional given?
 
  • #4
mynameisfunk said:
Had a SAT level geometry question from a student and didn't know how to solve it. I redrew what the picture was and the question asked for the slope. I know PF better than that but don't just give me the answer bc I need to know how to solve.

The equation of a line is [itex]y=ax+b[/itex] for some unknown constants a and b. Since we are given the value of one of the points, (x,y)=(3,4) then plugging it into this equation yields [itex]4=3a+b[/itex]

Just one more equation and then we can solve for a and b simultaneously. Good luck!
 

1. What is a "SAT level slope question"?

A "SAT level slope question" is a type of question that is commonly seen on the math section of the SAT exam. It requires the test-taker to use their knowledge of slope, or the steepness of a line, to solve a problem.

2. How do I solve a "SAT level slope question"?

To solve a "SAT level slope question", you will need to use the formula for slope, which is rise over run (also known as change in y over change in x). You will also need to be familiar with the concept of slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

3. What types of problems might I encounter in a "SAT level slope question"?

You may encounter problems that ask you to find the slope of a line, determine the equation of a line given two points, or use slope to solve a real-world problem. You may also encounter questions that test your understanding of parallel and perpendicular lines.

4. How can I prepare for "SAT level slope questions"?

To prepare for "SAT level slope questions", it is important to review the formula for slope and practice solving problems that involve finding slope or using slope to solve a problem. You can also take practice tests or work on sample problems to improve your skills.

5. Are there any tips for solving "SAT level slope questions" quickly and accurately?

One tip for solving "SAT level slope questions" quickly and accurately is to make sure you understand the problem before diving into the solution. Read the question carefully and identify what information is given and what you are being asked to find. It can also be helpful to draw a diagram or graph to visualize the problem. Additionally, practice and familiarity with the concepts will help you solve these types of questions more efficiently.

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