Question

How do you find c in a linear equation?

Answer 1

Hint: A straight line's general equation is \[y = mx + c\], where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. \[y = mx + c\], represents the equation of a straight line with gradient m and intercept c on the y-axis.

Formula used:
The slope intercept of line is \[y = mx + c\].

Complete step by step Solution:
We know that, c of a linear equation denotes the y-intercept of linear equation.
If an equation in the form \[\dfrac{x}{a} + \dfrac{y}{b} = 1\].
The y-intercept of the linear equation is \[b\].
The value of c is equal to b.

The slope-intercept form of a linear equation is \[y = mx + c\].
The y intercept of the linear equation is c.

If a linear equation is in the form \[mx + ny = l\].
Subtract \[mx\] from both sides of the equation:
\[mx + ny - mx = l - mx\]
\[ \Rightarrow ny = l - mx\]
Divide both sides by n:
\[ \Rightarrow y = - \dfrac{m}{n}x + \dfrac{l}{n}\]
Compare the above equation with \[y = mx + c\]
\[c = \dfrac{l}{n}\]
The y-intercept of \[mx + ny = l\] or the value of c is \[\dfrac{l}{n}\].
Additional information: A linear equation is an equation such that the highest power of the variable or variables is 1.
The linear equation with one variable is \[y = a\].
The linear equation with two variables is \[ax + by = c\].
The linear equation with three variables is \[ax + by + cz = d\].

Note: Students often confused with y-intercept and x-intercept. The x-intercept of mx+ny=l is \[\dfrac{l}{m}\] and y-intercept is \[\dfrac{l}{n}\].