Question

Find the y-intercept of the following function: 2x - 4y = 9​

Answer 1

$\large\underline{\sf{Solution-}}$

Given linear equation is

$\rm :\longmapsto\:2x - 4y = 9$

can be rewritten as

$\rm :\longmapsto\: - 4y = 9 - 2x$

Multiply by - 1, both sides, we get

$\rm :\longmapsto\: 4y = 2x - 9$

On dividing by 4, both sides, we get

$\rm :\longmapsto\:y = \dfrac{x}{2} - \dfrac{9}{4}$

We know,

Slope - intercept form of a line is given by y = mx + c,

where,

m is slope of line

c is intercept on y - axis.

So, on comparing

$\rm :\longmapsto\:y = \dfrac{x}{2} - \dfrac{9}{2}$

with

$\rm :\longmapsto\:y = mx + c$

So,

$\rm \implies\:\boxed{ \tt{ \: c \: = \: - \: \frac{9}{4} \: }}$

Additional Information :-

Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

Equation of the lines which is parallel to the X-axis is y = a

and

Equation of a line which is parallel toY-axis is x = a,

2. Point-slope form

Consider a line which passes through the point  P(a, b) having slope m, then equation of line is given by

y - b = m(x - a)

3. Slope-intercept form

Consider a line whose slope is m which cuts the Y-axis at a distance ‘c’ from the origin, then equation of line is given by y = mx + c

4. Intercept Form of Line

Consider a line which makes an intercept of a units and b units on x - axis and y - axis respectively, then equation of line is given by x/a + y/b = 1.

5. Normal form of Line

Consider a perpendicular from the origin having length p  and it makes an angle β with the positive X-axis.

Then, equation of line is given by x cosβ + y sinβ = p.