Question

Write an equation of the line in slope-intercept form.

Answer 1

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

What does this problem want us to find:

$\hookrightarrow \text{The slope-intercept form}: y= mx + b$

• m : slope
• b: y-intercept

Let's find the slope:

• (x₁, y₁)  ⇒ 0,3)
• (x₂, y₂) ⇒ (4,2)

    $m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{2-3}{4-0} =-\dfrac{1}{4}$

Let's find the y-intercept:

 ⇒ the value of the y-coordinate when the x-coordinate value is '0'

    ⇒ thus it is '3'

Our equation is:

 $y=-\dfrac{1}{4} x+3$    <=====  Answer

Hope that helps!

#LearnwithBrainly

     

Answer 2

Greetings from Brasil...

One way to solve this question is through a determinant.

| X     Y     1 |

| X₁    Y₁    1 |  = 0

| X₂    Y₂   1 |

as

(X₁; Y₁) = (0; 3)

(X₂; Y₂) = (4; 2)

then

| X   Y  1 |

| 0   3   1 |  = 0

| 4   2   1 |

4Y + X - 12 = 0