Question

Find the equation of the line through the points (-9,6) and (1,27).

Answer 1

Answer:

$y=\frac{21}{10} x + \frac{249}{10}$

Step-by-step explanation:

Pre-Solving

We are given the points (-9, 6), and (1, 27).

We want to find the equation of the line through these points.

There are three ways to write the equation of the line:

• Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept
• Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0. a is usually non-negative as well.
• Point-slope form, which is $y-y_1=m(x-x_1)$, where m is the slope and $(x_1, y_1)$ is a point.

All of these three ways are equally valid ways to write the equation of the line.

However, let's write the equation in slope-intercept form, as it is the most common way to write it.

Solving

Slope

First, we need to find the slope.

The slope (m) can be calculated using the formula $m=\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points.

We can label the values of our points to avoid any confusion and mistakes.

$x_1=-9\\y_1=6\\x_2=1\\y_2=27$

Substitute these into our formula. Remember that we have negative numbers.

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

$m=\frac{27-6}{1--9}$

Simplify.

$m=\frac{27-6}{1+9}$

Combine the numbers.

$m=\frac{21}{10}$

We found the slope.

y-intercept

We can plug our value of the slope into the formula for slope-intercept.

$y=\frac{21}{10} x + b$

However, we now need to find b.

As the points (-9, 6) and (1, 27) pass through the line, we can use their values to solve for b.

Either point will work for this case; they will both lead to the same answer.

Taking (-9,6) for example:

Substitute -9 as x and 6 as y.

$6=\frac{21}{10}(-9) + b$

Multiply

$6=-\frac{189}{10} + b$

Add -189/10 to both sides.

$6+\frac{189}{10} = b$

$\frac{249}{10} = b$

Substitute 249/10 as b in the equation.

$y=\frac{21}{10} x + \frac{249}{10}$

Topic: finding the equation of the line

See more: brainly.com/question/25508767

Answer 2

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept

The formula for calculating slope is expressed as

m = (y2 - y1)/(x2 - x1)

From the information given, the line passes through an initial point of (- 9, 6) and (1, 27). This means that

x1 = - 9, y1 = 6

x2 = 1, y2 = 27

By substituting these values into the slope formula, we have

m = (27 - 6)/(1 - - 9) = 21/(1 + 9) = 21/10

We would find the y intercept by substituting m = 21/10, x = - 9 and y = 6 into the slope intercept equation. We have

6 = 21/10 * - 9 + c = - 189/10 + c

c = 6 + 189/10 = 249/10

By substituting m = 21/10 and c = 249/10 into the slope intercept equation, the equation of the line is

y = 21x/10 + 249/10

In decimal form, the equation of the line is

y = 2.1x + 24.9