Question

Find the equation of the line that has an intercept at \[x = - 4\] and intercept at \[y = 5\].

Answer 1

Hint: In this problem first put values of a and b to find the required equation of line.
The intercept of a line is the point at which it intersects either the \[x\]- axis or \[y\]- axis. In the above question \[x\] intercept & \[y\]- intercept are given at \[x = - 4\] & \[y = 5\] respectively. The equation of the line, which intersects the \[y\]- axis at a point is given by \[y = mx + c\] . The formula for the intercept of al line is given by \[c = y - mx\]
The equation of line in the form of intercept when the line is intersecting the \[x\]- axis and \[y\]- axis at point \[a\] &\[b\] respectively.
\[\dfrac{x}{a} + \dfrac{y}{b} = 1\]
Here, ‘\[a\]’ and ‘\[b\]’ are the intercepts of the line which intersect the \[x\]- axis and \[y\]- axis respectively.

Complete step-by-step answer:
Given intercepts:
\[x\]-intercepts at \[x = - 4\] ……. (a)
\[y\]-intercepts at \[y = 5\] ……. (b)
We know that
Eqn of line in intercept form.
\[\dfrac{x}{a} + \dfrac{y}{b} = 1\] ……. eqn (i)
Putting the values \[a = - 4\], \[b = 5\]
In equation (i)
Required eqnof line \[ \Rightarrow\dfrac{x}{{ - 4}} + \dfrac{y}{5} = 1\]
\[ \Rightarrow\dfrac{{ - x}}{4} + \dfrac{y}{5} = 1\]
\[ \Rightarrow\dfrac{{ - 5x + 4y}}{{20}} = 1\]
\[ \Rightarrow - 5x + 4y = 20\]
\[ \Rightarrow 4y - 20 = 5x\]

$5x-4y+20=0$ is the required line equation.

Note: The values of ‘\[a\]’ and ‘\[b\]’ can be positive, negative or zero and explain the position of the points at which the line cuts both axes, relative to the origin. General form of a straight line is $ax+by+c=0.$