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

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To determine the equation of a line given one point and an unknown value, it is essential to know the coordinates of two points to calculate the slope. The equation of a line is expressed as y=ax+b, where a represents the slope and b the y-intercept. With one known point, such as (3,4), substituting into the equation gives 4=3a+b. Additional information, like the point of intersection bisecting the line segment between the axes, could provide the necessary second point for solving. Without sufficient data, the problem remains unsolvable.
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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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