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Monica [59]
2 years ago
8

Please help! I need this quickly

Mathematics
1 answer:
Lera25 [3.4K]2 years ago
4 0

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.

<u>x + 3y = 30</u>

<u></u>

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

See more: brainly.com/question/27575555

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