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

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Homework Help Overview

The discussion revolves around finding the equation of a line given one point and an unknown value, specifically focusing on the slope in the context of a geometry problem typically encountered in standardized tests like the SAT.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of having two points to determine the slope and question whether additional information about the line's characteristics is provided, such as a point of intersection or specific coordinates.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the problem and questioning the adequacy of the provided information. Some guidance has been offered regarding the relationship between points and the equation of a line, but no consensus has been reached.

Contextual Notes

There is mention of a specific point given in the problem, but the lack of a second point or additional constraints is noted as a limitation in solving for the slope.

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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There is not enough information on the picture. You need to specify the coordinates of two points to get the slope.
 
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?
 
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 y=ax+b 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 4=3a+b

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

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