Question

Write the equation of the line with two given points

(-12, 14) and (6,-1)

Answer 1

Answer:

y= -5/6x + 4

Step-by-step explanation:

um use slope equation to find slope equal to -5/6, then plug in the point (6,-1) to get the y intercept as 4

Answer 2

Answer:

y=-5/6x+4

Step-by-step explanation:

Hi there!

We are given the points (-12, 14) and (6,-1)

We want to write the equation of the line using those points

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
• 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
• Standard form, which is ax+by=c, where a, b, and c are integer coefficients, but a and b cannot be 0 and a cannot be negative

First, let's find the slope of the line:

The formula for the slope calculated from 2 points is $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have 2 points, which is what we need to calculate the slope, but let's label the values of the points to avoid confusion.

$x_1=-12\\y_1=14\\x_2=6\\y_2=-1$

Now substitute those values into the equation to solve for m (the slope)

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

m=$\frac{-1-14}{6--12}$

Simplify the fraction

m=$\frac{-15}{6+12}$

Add the numbers on the denominator together

m=$\frac{-15}{18}$

Simplify the fraction

m=-5/6

Now that we know the slope, we can use slope-intercept form or point-slope form to find the equation of the line

The most common way is write it in slope-intercept form, though, so let's do it that way.

Substitute -5/6 as m in y=mx+b

y=-5/6x+b

Now we need to find b

As the equation passes through the points  (-12, 14) and (6,-1), we can use either one of them to help solve for b

Taking (6, -1) for example, substitute its values into the equation:

-1=-5/6(6)+b

Multiply

-1=-5+b

Add 5 to both sides

4=b

Substitute 4 as b into the equation

y=-5/6x+4

Hope this helps!