SOLUTION: An equation of a line is y=5/3x+c. Determine the value of c when the line passes through the point F(4,-6). Describe your strategy.

Algebra ->  Linear-equations -> SOLUTION: An equation of a line is y=5/3x+c. Determine the value of c when the line passes through the point F(4,-6). Describe your strategy.      Log On


   

Question 795462: An equation of a line is y=5/3x+c. Determine the value of c when the line passes through the point F(4,-6). Describe your strategy.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The given equation has three variables. Your given point, F, will give values to the variables x and y, leaving only the variable c as unknown. You would then just solve for c and simplify.

A clear method which you can choose, is solve for c FIRST. Substitute the values from F into the formula for c and evaluate.


Performing that described method:
y=%285%2F3%29x%2Bc. Point F on the line is given as (4,-6).
Solving for c,
c=y-%285%2F3%29x
Substituting with point F,
c=-6-%285%2F3%294
c=-6-20%2F3
c=%28-18-20%29%2F3
highlight%28c=-38%2F3=-12%262%2F3%29

The equation in the two variables x and y, is highlight%28y=%285%2F3%29x-12%262%2F3%29

Drawing the graph is just a matter of indicating the y-intercept, which is c in your equation, and using the slope, 5%2F3.
Note, knowing the given point F, you can also graph the line by indicating (4,-6) on the cartesian plane and using the slope, 5%2F3. In this way, if you make your axes suitably, you can read the y-intercept directly from the graphed line.