Question

Find an equation of the line in the form ax+by=c whose​ x-intercept is 12 and​ y-intercept is 4​, where​ a, b, and c are integers with no factor common to all​ three, and greater than or equal 0.

Answer 1

Answer:

The equation of the line  in $ax+by=c$  form where $a,b,c$  are integers with no factor common to all​ three, and greater than or equal 0 is:

$x+3y=12$

Step-by-step explanation:

Given:

x-intercept = 12

y-intercept = 4

To find the equation of line in the form $ax+by=c$ where $a,b,c$  are integers with no factor common to all​ three, and greater than or equal 0.

Solution:

The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as $(x,0)$

Thus, on point of the line is (12,0)

The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as $(0,y)$.

Thus, on point of the line is (0,4)

Using the two points we can find the slope of the line using the slope formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

So, slope of the line can b given as:

$m=\frac{4-0}{0-12}$

$m=\frac{4}{-12}$

$m=-\frac{1}{3}$

The slope intercept form of the equation of he line is given as:

$y=mx+b$

where $m$ represents slope of the line and $b$ represents the y-intercept.

So, the equation of the line can be given as:

$y=-\frac{1}{3}x+4$

Multiplying each term by 3 to remove fraction.

$3y=3.-\frac{1}{3}x+4(3)$

$3y=-x+12$

Adding $x$ both sides.

$3y+x=-x+x+12$

$3y+x=12$

Thus, the equation of the line  in $ax+by=c$  form where $a,b,c$  are integers with no factor common to all​ three, and greater than or equal 0 is:

$x+3y=12$

Answer 2

The equation of the line is $x + 3y = 4$

Linear equation

A linear equation is used to model functions that have constant rates

The form of the linear equation is given as:

$ax + by = c$

From the intercepts, we have the following points

(12, 0) and (0,4)

Start by calculating the slope (m)

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{4 -0}{0-12}$

$m = -\frac{1}{3}$

The equation is then calculated as:

$y = m(x -x_1) + y_1$

So, we have:

$y =-\frac 13(x -0) + 4$

$y =-\frac 13x + 4$

Multiply through by 3

$3y = -x + 4$

Add x to both sides

$x + 3y = 4$

Hence, the equation of the line is $x + 3y = 4$

Read more about linear equations at:

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