131k views
0 votes
Find the equation of the line given (3,4) and (-1,8)

(help. i don't know what i did to get the incorrect answer. i got -1x+y=1, but it's wrong)​

1 Answer

5 votes

Answer:

Slope intercept form is y = -x+7

Standard form is x+y = 7

Both forms represent the same line, just written in different ways of course.

The graph is shown below.

=====================================================

Step-by-step explanation:

Let's check the answer you got.

The equation -1x+y=1 is the same as -x+y = 1

Plug the coordinates of the first point into this equation

-x+y = 1

-3+4 = 1

1 = 1

The first point is on the line -x+y = 1

Repeat similar steps for the other point

-x+y = 1

-(-1)+8 = 1

1+8 = 1

9 = 1

The two sides don't match up. We need the same number on both sides to get a true equation. The false equation tells us that (-1,8) is not on the line -x+y = 1.

In short, this rules out -x+y = 1 being the answer.

The next section will show one way to find the answer.

--------------------------------

First we'll need the slope of the line through (3,4) and (-1,8)


(x_1,y_1) = (3,4) \text{ and } (x_2,y_2) = (-1,8)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (8 - 4)/(-1 - 3)\\\\m = (4)/(-4)\\\\m = -1\\\\

Then I'll use the y = mx+b template to find b. For the (x,y), use either point given to you. I'll use (3,4).

So,

y = mx+b

4 = -1*3+b

4 = -3+b

4+3 = b

7 = b

b = 7

We found that m = -1 and b = 7.

We go from y = mx+b to y = -1x+7 aka y = -x+7 which is the answer in slope intercept form.

To convert to standard form Ax+By = C, add x to both sides. The goal is to get the variable terms to one side, and the constant isolated on its own side.

y = -x+7

y+x = -x+7+x

x+y = 7 is the answer in standard form

--------------------------------

Check:

Plug (x,y) = (3,4) into the equation to see if we get a true result.

x+y = 7

3+4 = 7

7 = 7

That works out. Now do the other pair of coordinates (-1,8).

x+y = 7

-1+8 = 7

7 = 7

That works as well. The answers are fully confirmed to be correct.

If you wanted, you can use the equation y = -x+7 as the way to check the answer. It's up to you which you prefer better if it's slope-intercept or standard form.

Yet another way to check the answer is to use a graphing tool like GeoGebra. It's something I use all the time. See the screenshot diagram below.

Find the equation of the line given (3,4) and (-1,8) (help. i don't know what i did-example-1
User Balualways
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories