Question

Find the equation of a line that contains the points (1,−6) and (−8,−1).

(Write the equation in standard form.)

Answer 1

Answer:

5x+9y=-49

Step-by-step explanation:

Hi there!

We want to find the equation of a line that contains the points (1, -6) and (-8, -1), and we want it to be in standard form.

Standard form is ax+by=c, where a, b, and c are integer coefficients, but a and b CANNOT equal 0 or be negative

To get the line into standard form, it's helpful to first put it in a different form, like slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Let's start by finding the slope; we can calculate it from two points by using the equation $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have two points, but let's label the values of the points to avoid any confusion:

$x_1=1\\y_1=-6\\x_2=-8\\y_2=-1$

Now substitute those values in the formula:

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

m=$\frac{-1--6}{-8-1}$

Simplify:

m=$\frac{-1+6}{-8-1}$

Add the numbers together:

m=$\frac{5}{-9}$

The slope is -5/9

Here is the equation so far:

y=-5/9x+b

Now we need to find b

Since the equation passes through both (1, -6) and (-8, -1), we can use either one of them to solve for b

Taking (-8, -1) for example:

-1=-5/9(-8)+b

Multiply

-1=40/9+b

Subtract 40/9 from both sides

-49/9=b

Substitute -49/9 as b in the equation:

y=-5/9x-49/9

This is the equation in slope-intercept form

Now, remember how we wanted to get the equation into standard form, which is ax+by=c.

So let's move -5/9x to the left side

5/9x+y=-49/9

Remember that we want the coefficients a, b, and c to be integers, so multiply both sides by 9:

5x+9y=-49

Hope this helps!