Question

What is an equation of the line that passes through the points (3,6) and (1,−2)?

Answer 1

Answer:

y = 4x - 6

Step-by-step explanation:

Hi there!

We are given the points (3,6) and (1, -2), and that a line passes through these 2 points

We want to find the equation of said line

There are 3 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 integer coefficients but a and b cannot be equal to 0, and a cannot be negative
• Slope-point form, which is $y-y_1=m(x-x_1)$, where m is the slope and $(x_1, y_1)$ is a point

The  most common way is slope-intercept form, so let's write the equation of the line this way

First, we need to find the slope

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

Before we calculate, let's label the values of the points.

$x_1=3\\y_1=6\\x_2=1\\y_2=-2$

Now substitute into the formula

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

m=$\frac{-2-6}{1-3}$

Subtract

m=$\frac{-8}{-2}$

Divide

m= 4

The slope of the line is 4

Substitute 4 as m in y=mx+b:

y = 4x + b

Now to find b

Since the equation passes through both (3,6) and (1, -2), we can use either point to help solve for b.

Taking (3,6) for example:

Substitute 3 as x and 6 as y.

6 = 4(3) + b

Multiply

6 = 12 + b

Subtract 12 from both sides

-6 = b

Substitute -6 as b into the equation

y = 4x - 6

Hope this helps!

Topic: finding the equation of the line

See more here: brainly.com/question/27618860