Find the values of a and b in the given straight line equation

In summary, the coordinates for the problem are (a,0) and (0,b), where ##a=2\sqrt{10}## and ##b=6\sqrt{10}##. The gradient is calculated to be -3 using the given equations, leading to the equation 400=9a^2+a^2. Another approach was suggested, with the same result.
  • #1
chwala
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Homework Statement
see attached
Relevant Equations
straight lines
Find the problem below;
1640819951710.png


My approach,
if##x=0##, then ##y=b## and if ##y=0##, then ##x=a##, therefore our co-ordinates are ##(a,0)## and ##(0,b)##. The gradient will give us,
$$-3=\frac {b-0}{0-a}$$
It follows that, ##b=3a##, therefore
$$20=\sqrt {(3a-0)^2+(0-a)^2}$$
$$400=9a^2+a^2$$
##a=2\sqrt 10## and ##b=6\sqrt 10##

Any other approach on this.
 
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  • #2
chwala said:
##a=2\sqrt 10## and ##y=6\sqrt 10##

Any other approach on this?

I'm pretty sure you mean the ##b=6\sqrt{10}## .

My approach was about the same as yours.
 
Last edited:
  • #3
SammyS said:
I'm pretty sure you mean the ##b=6\sqrt{10}## .

My approach was about the same as yours.
Sammy happy new year 2022 Mate!Let me amend it, sure.
 
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Likes SammyS

FAQ: Find the values of a and b in the given straight line equation

1. What is the formula for a straight line equation?

The formula for a straight line equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

2. How do I find the slope of a straight line?

The slope of a straight line can be found by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.

3. How do I find the y-intercept of a straight line?

The y-intercept of a straight line can be found by setting x = 0 in the equation y = mx + b and solving for b.

4. What information do I need to find the values of a and b in a straight line equation?

To find the values of a and b in a straight line equation, you will need the slope of the line and the coordinates of at least one point on the line.

5. Can I use any two points on a straight line to find the values of a and b?

Yes, any two points on a straight line can be used to find the values of a and b, as long as they are not the same point and the line is not vertical (in which case the slope would be undefined).

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