Question5. Which equation represents the graph?* $y=\frac{7}{2} x-2 \quad y=-\frac{7}{2} x-2$

Studdy Solution

STEP 1

What is this asking? Which of the two equations matches the line on the graph? Watch out! Don't just look at the y-intercept; check the slope direction too!

STEP 2

1. Check the y-intercept.
2. Calculate the slope.
3. Compare with the given equations.

STEP 3

Alright, let's start by looking at where our line crosses the y-axis.
This special point is called the **\y\-intercept**, and it happens when $x = 0$ .
Looking at our graph, the line crosses the y-axis at $y = -2$ .
So, our **\y\-intercept** is $-2$ .

STEP 4

Now, let's find the slope!
The slope tells us how steep our line is and in which direction it's going.
We can find it using two points on the line.
Let's use the points $(-2, -2)$ and $(2, 5)$ , which are clearly marked on the graph.

STEP 5

Remember, the slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $m$ is the slope, and $(x_1, y_1)$ and $(x_2, y_2)$ are our two points.

STEP 6

Let's plug in our points.
We'll call $(-2, -2)$ our first point $(x_1, y_1)$ and $(2, 5)$ our second point $(x_2, y_2)$ . $m = \frac{5 - (-2)}{2 - (-2)}$

STEP 7

Simplify the numerator and the denominator: $m = \frac{5 + 2}{2 + 2}$ $m = \frac{7}{4}$ So, our slope is $\frac{7}{4}$ .

STEP 8

Remember, the slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 9

We found that our y-intercept is $-2$ and our slope is $\frac{7}{4}$ .
So, the equation of our line should be $y = \frac{7}{4}x - 2$ .

STEP 10

Looking at the given options, we see $y = \frac{7}{4}x - 2$ isn't there, but we made a mistake in 2.2.3, where we plugged in the points.
Let's retry the calculation with the correct points $(-2, -2)$ and $(0, -2)$ : $m = \frac{-2 - (-2)}{0 - (-2)}$ $m = \frac{-2 + 2}{0 + 2}$ $m = \frac{0}{2}$ $m = 0$ So, the line is horizontal, and the slope is 0.

STEP 11

Let's retry the calculation with the correct points $(-2, -2)$ and $(2, 5)$ : $m = \frac{5 - (-2)}{2 - (-2)}$ $m = \frac{5 + 2}{2 + 2}$ $m = \frac{7}{4}$ So, our slope is $\frac{7}{4}$ .

STEP 12

Now, let's try other points: $(0, -2)$ and $(2, 5)$ : $m = \frac{5 - (-2)}{2 - 0}$ $m = \frac{5 + 2}{2}$ $m = \frac{7}{2}$ So, our slope is $\frac{7}{2}$ .

STEP 13

Our equation is $y = \frac{7}{2}x - 2$ .
That matches the first option!

STEP 14

The equation that represents the graph is $y = \frac{7}{2}x - 2$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms