Question

Please help! I need this quickly

Answer 1

Answer:

x + 3y = 30

Step-by-step explanation:

We are given that a line contains the points (12,6) and (-3,11)​.

We want to write the equation of this line in standard form.

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.

Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

So first, let's find the slope of the line.
The slope (m) can be found using the formula $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points.

Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.

$x_1=12\\y_1=6\\x_2=-3\\y_2=11$

Now substitute these values into the formula.

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

m=$\frac{11-6}{-3-12}$

Subtract

m=$\frac{5}{-15}$

Simplify

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

The slope is -1/3

Here is the equation of the line so far in slope-intercept form:

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

We need to solve for b.

As the equation passes through (12,6) and (-3,11)​, we can use either one to help solve for b.

Taking (12, 6) for example:

$6=-\frac{1}{3}(12) + b$

Multiply

$6=-\frac{12}{3} + b$

Divide

6 = -4 + b

Add 4 to both sides.

10 = b

Substitute 10 as b in the equation.

$y = -\frac{1}{3} x + 10$

Here is the equation in slope-intercept form, but remember, we want it in standard form.

In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.

$\frac{1}{3} x + y = 10$

Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.

So, let's multiply both sides by 3 to clear the fraction.

$3(\frac{1}{3} x + y) = 3(10)$
Multiply.

x + 3y = 30

Topic: finding the equation of the line (standard form)

See more: brainly.com/question/27575555