Different forms of linear equations

In summary, the two forms of linear equations, a x + b y = c and y = m x + c, are equivalent to each other. However, the coefficients and constants in the equations must be numerically different for the equations to be truly equal.
  • #1
Beam me down
47
0
A while back in maths we were introduced to the linear equation in two forms:

[tex]a x + b y = c[/tex] (1)

[tex]y = m x + c[/tex] (2)

Now I can use both forms of these, but I was told that:

[tex] y = m x + c \Leftrightarrow a x + b y = c [/tex]

where [tex]m = \frac{a}{b} [/tex]

Thiis can't be right can it? As:

[tex]a x + b y = c [/tex]

[tex] b y = c - a x [/tex]

[tex] y = \frac{c}{b} - \frac{a x }{b}[/tex]
 
Last edited:
Physics news on Phys.org
  • #2
Obviously the c's in equations 1 and 2 are not the same. They cannot be as you have demonstrated.

Using [tex] y = \frac{c}{b} - \frac{a x }{b}[/tex]

and [tex]y = m x + d[/tex],

then m = [tex]-\frac{a}{b}[/tex] and

d = [tex]\frac{c}{b}[/tex]
 
  • #3
Astronuc said:
Obviously the c's in equations 1 and 2 are not the same. They cannot be as you have demonstrated.

Thanks. My teacher was saying the two forms are the same (ie: at least "c" in both equations are the same). I couldn't prove it, and nor could she, and we both forgot about it.
 
  • #4
Both equations represent a line, but the coefficients must be numerically different.

Basically, one is dividing all terms in (1) by the coefficient (b) of y, and to be equal, the m = - (a/b) and c in equation 2 must be c/a, so the c's must be different.
 

1. What are the different forms of linear equations?

The three most common forms of linear equations are standard form, slope-intercept form, and point-slope form.

2. How do I convert an equation from standard form to slope-intercept form?

To convert from standard form to slope-intercept form, you can use the following steps:

  1. Isolate the y variable on one side of the equation.
  2. Divide both sides of the equation by the coefficient of the y variable.
  3. If necessary, simplify the fraction.
  4. The resulting equation will be in the form y = mx + b, where m is the slope and b is the y-intercept.

3. What is the difference between point-slope form and slope-intercept form?

The main difference between point-slope form and slope-intercept form is that point-slope form uses a specific point and slope to define the line, while slope-intercept form uses the slope and y-intercept to define the line.

4. Can you graph a linear equation in standard form?

Yes, you can graph a linear equation in standard form. To graph a linear equation in standard form, you can use the following steps:

  1. Isolate the y variable on one side of the equation.
  2. Find the x and y intercepts by setting y = 0 and solving for x, and setting x = 0 and solving for y.
  3. Plot these points on a coordinate plane and connect them with a straight line to create the graph of the equation.

5. How do I determine the slope of a linear equation?

The slope of a linear equation is represented by the coefficient of the x variable. In slope-intercept form, the slope is equal to the coefficient of x. In standard form, you can find the slope by rearranging the equation to solve for y and then dividing the coefficient of x by the coefficient of y.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
5
Views
634
  • Precalculus Mathematics Homework Help
Replies
17
Views
908
  • Precalculus Mathematics Homework Help
Replies
1
Views
466
  • Precalculus Mathematics Homework Help
Replies
2
Views
765
  • Precalculus Mathematics Homework Help
Replies
5
Views
943
  • Precalculus Mathematics Homework Help
Replies
5
Views
928
  • Precalculus Mathematics Homework Help
Replies
5
Views
721
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
8
Views
322
Back
Top