Question

3)Find the slope of line whose
x-intercept is -2 and y-
intercept is 3​

Answer 1

$\large\underline{\bold{Given \:Question - }}$

• Find the slope of line whose x-intercept is -2 and y- intercept is 3

$\large\underline{\bold{ANSWER- }}$

$\large\underline{\bold{Given- }}$

• A line whose x-intercept is -2 and y- intercept is 3

$\large\underline{\bold{To\:Find - }}$

• Slope of line

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

We know,

• The equation of line having x - intercept 'a' and y - intercept 'b' is given by

$\rm :\longmapsto\:\dfrac{x}{a} + \dfrac{y}{b} = 1$

Now,

Here,

• Intercept on x - axis, a = - 2

and

• Intercept on y - axis, b = 3

So,

• Equation of line is given by

$\rm :\longmapsto\:\dfrac{x}{ - 2} + \dfrac{y}{3} = 1$

$\rm :\longmapsto\: - 3x + 2y = 6$

$\rm :\longmapsto\:2y = 3x + 6$

$\rm :\longmapsto\:y = \dfrac{3}{2} x + 3$

• On comparing with y = mx + c, we get

$\bf :\longmapsto\:m \: = \: \dfrac{3}{2}$

$\bf\implies \:slope \: of \: line, \: m \: = \: \dfrac{3}{2}$

Additional Information

Additional Information Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

• Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line.

• Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line.

2. Point-slope form equation of line

• Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by y - b = m(x - a)

3. Slope-intercept form equation of line

• Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by y = mx + a.

4. Intercept Form of Line

• Consider a line L having x– intercept a and y– intercept b, then the line passes through  X– axis at (a,0) and Y– axis at (0,b). 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 to line L and it makes an angle β with the positive X-axis. Then, equation of the line is given by x cosβ + y sinβ = p.