Question

what is the equation in the slope intercept form of the line that passes through the points (-4,2)and (12,6)

Answer 1

Given Point

A(-4,2) and B(12,6)

To Find Equation in the slope Intercept form

Formula

(y-y₁) = m(x-x₁)

Formula to find Slope(m)

m = (y₂ - y₁)/(x₂ - x₁)

We have

x₁ = -4 , y₁ = 2 , x₂ = 12 and y₂ = 6

Now Find Slope

m = (6 - 2)/(12 + 4)

m = 4/16

m = 1/4

Now Put the value on

(y - y₁) = m(x - x₁)

(y - 2) = 1/4(x + 4)

4(y - 2) = 1(x + 4)

4y - 8 = x + 4

x - 4y + 4 + 8 = 0

x - 4y + 12 = 0

Answer

Equation → x - 4y + 12 = 0

Answer 2

Answer:

Given :-

• The slope intercept form of the line passes through the points of (- 4 , 2) and (12 , 6).

To Find :-

• What is the equation in the slope intercept.

Formula Used :-

$\clubsuit$ Slope Formula :

$\longmapsto \sf\boxed{\bold{\pink{m =\: \dfrac{y_2 - y_1}{x_2 - x_1}}}}$

where,

• m = Slope
• (x₁ , y₁) = Co-ordinates of first point in the line
• (x₂ , y₂) = Co-ordinates of second point in the line

$\clubsuit$ Point-Slope Formula :

$\longmapsto \sf\boxed{\bold{\pink{y - y_1 =\: m(x - x_1)}}}$

where,

• m = Slope
• (x , y) = Variables
• (y₁ , x₁) = Co-ordinates of a points on a line

Solution :-

➤ First, we have to find the value of m :

Given points :

$\mapsto$ (- 4 , 2)

$\mapsto$ (12 , 6)

Then,

• x₁ = - 4
• x₂ = 12
• y₁ = 2
• y₂ = 6

According to the question by using the formula we get,

$\implies \sf m =\: \dfrac{6 - 2}{12 - (- 4)}$

$\implies \sf m =\: \dfrac{4}{12 + 4}$

$\implies \sf m =\: \dfrac{\cancel{4}}{\cancel{16}}$

$\implies \sf\bold{\green{m =\: \dfrac{1}{4}}}$

➤ Now, we have to find the equation in the slope intercept :

Given :

• x₁ = - 4
• y₁ = 2
• m = ¼

According to the question by using the formula we get,

$\implies \sf (y - 2) =\: \dfrac{1}{4}(x - \{- 4\})$

$\implies \sf (y - 2) =\: \dfrac{1}{4}(x + 4)$

By doing cross multiplication we get,

$\implies \sf 4(y - 2) =\: 1(x + 4)$

$\implies \sf 4y - 8 =\: x + 4$

$\implies \sf x + 4 - 4y + 8 =\: 0$

$\implies \sf x - 4y + 4 + 8 =\: 0$

$\implies \sf\bold{\red{x - 4y + 12 =\: 0}}$

$\therefore$ The equation in the slope intercept is x - 4y + 12 = 0.