Question

Please help me with these questions

Answer 1

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

$\spadesuit\; Slope(m) = \frac{y_1 - y_2}{x_1 - x_2}$

Given Points are (8 , 30) and (18 , 60)

here x₁ = 8 and x₂ = 18 and y₁ = 30 and y₂ = 60

$\spadesuit\; Slope(m) = \frac{30 - 60}{8 - 18} = \frac{-30}{-10} = 3$

We know that the form of line passing through point (x₀ , y₀) and having slope m is : y - y₀ = m(x - x₀)

Here the line passes through the point (8 , 30)

⇒ x₀ = 8 and y₀ = 30

We found Slope(m) = 3

Substituting all the values in the standard form, We get :

Equation of the line : y - 30 = 3(x - 8)

Let d be the x-intercept of this line

⇒ The line passes through the point (d , 0) as at x-intercept, y-coordinate is zero.

⇒ 0 - 30 = 3(d - 8)

⇒ 3d - 24 = -30

⇒ 3d = -30 + 24

⇒ 3d = -6

⇒ d = -2

⇒ The x - coordinate of the x-intercept of the line is -2