Question

Write an equation in standard form for the line that passes through the given points.

Answer 1

Answer:

The equation of the line in standard form is $3x+2y=12$

Step-by-step explanation:

we know that

The equation of the line in standard form is

$Ax+By=C$

where

A is a positive integer

B and C are integers

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

(0,6) and (4.0)

substitute the values

$m=\frac{0-6}{4-0}$

$m=\frac{-6}{4}$

$m=-\frac{3}{2}$

step 2

Find the equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

we have

$m=-\frac{3}{2}$

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem the y-intercept is given

The y-intercept is the point (0,6)

so

$b=6$

substitute

$y=-\frac{3}{2}x+6$

step 3

Convert to standard form

Multiply by 2 both sides to remove the fraction

$2y=-3x+12$

Adds 3x both sides

$3x+2y=12$