Question

A line passes through the points (1, 4) and (2, 10). What is its equation in slope-intercept form?

Answer 1

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

Given that, a line passes through the points (1, 4) and (2, 10).

We know, Equation of line which passes through two points A(x₁, y₁) and B(x₂, y₂) is given by

$\color{green}\boxed{ \rm{ \: \: y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) \: }}$

So, here

$\rm \: x_1 = 1$

$\rm \: x_2 = 2$

$\rm \: y_1 = 4$

$\rm \: y_2 = 10$

So, on substituting the values in above expression, we get

$\rm \: y - 4 = \dfrac{10 - 4}{2 - 1}(x - 1)$

$\rm \: y - 4 = \dfrac{6}{1}(x - 1)$

$\rm \: y - 4 = 6(x - 1)$

$\rm \: y - 4 = 6x - 6$

$\rm \: y = 6x - 6 + 4$

$\rm \: y = 6x - 2$

Thus,

$\rm \:\rm\implies \: y = 6x - 2$

is the required equation of line in slope intercept form with slope = 6 and intercept on y axis is 2 units in the negative direction of y axis.

$\rule{190pt}{2pt}$

Additional Information :-

Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

Equation of line parallel to y - axis passes through the point (a, b) is x = a.

2. Point-slope form equation of line

Equation of line passing through the point (a, b) having slope m is y - b = m(x - a)

3. Slope-intercept form equation of line

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

4. Intercept Form of Line

Equation of line which makes an intercept of a and b units on x - axis and y - axis respectively is x/a + y/b = 1.

5. Normal form of Line

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle β with the positive X-axis is x cosβ + y sinβ = p.

Answer 2

Step-by-step explanation:

I hope this helps you bro and thanks