Math  /  Algebra

QuestionWrite the equation in point-slope form of the line shown below. A. y+2=45(x+3)y+2=\frac{4}{5}(x+3) B. y+2=54(x+3)y+2=\frac{5}{4}(x+3) C. y2=45(x3)y-2=\frac{4}{5}(x-3) D. y2=54(x3)y-2=\frac{5}{4}(x-3)
Write a linear equation in point - slope form that represents the values in the table

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line in point-slope form, given a graph and then again given a table of values. Watch out! Don't mix up the xx and yy coordinates, and be careful with the signs when using the point-slope form.

STEP 2

1. Find the Slope
2. Point-Slope Form (Graph)
3. Find the Slope (Table)
4. Point-Slope Form (Table)

STEP 3

Let's **find the slope** of the line from the graph!
We have two points: (3,2)(-3, -2) and (2,2)(2, 2).
Remember, slope is the *rise over run*, or how much the yy changes divided by how much the xx changes.

STEP 4

The **change in** yy is 2(2)=2+2=42 - (-2) = 2 + 2 = 4.
The **change in** xx is 2(3)=2+3=52 - (-3) = 2 + 3 = 5.

STEP 5

So, our **slope** is 45\frac{4}{5}.
Awesome!

STEP 6

The **point-slope form** of a line is yy1=m(xx1)y - y_1 = m(x - x_1), where mm is the **slope** and (x1,y1)(x_1, y_1) is any point on the line.
We can use either of our points.
Let's use (3,2)(-3, -2).

STEP 7

Plugging in our **slope** 45\frac{4}{5} and our **point** (3,2)(-3, -2), we get y(2)=45(x(3))y - (-2) = \frac{4}{5}(x - (-3)).
Simplifying this, we get y+2=45(x+3)y + 2 = \frac{4}{5}(x + 3).
This matches answer choice A!

STEP 8

Now, let's look at the table!
We need to find the slope again.
Pick any two points from the table.
Let's use (1, 2) and (2, 4).

STEP 9

The **change in** yy is 42=24 - 2 = 2.
The **change in** xx is 21=12 - 1 = 1.

STEP 10

So, the **slope** is 21=2\frac{2}{1} = 2.

STEP 11

Using the **point-slope form** yy1=m(xx1)y - y_1 = m(x - x_1) with our **slope** 22 and the **point** (1,2)(1, 2) (you could use any point from the table!), we get y2=2(x1)y - 2 = 2(x - 1).

STEP 12

For the graph, the equation in point-slope form is y+2=45(x+3)y + 2 = \frac{4}{5}(x + 3).
For the table, the equation is y2=2(x1)y - 2 = 2(x - 1).

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord