https://file.aiquickdraw.com/mathbot/file/1727034220642r1htnaba.jpg

To find the equation of the straight line shown in the graph, we need to express it in the form \( y = mx + c \), where:
- \( m \) is the slope (or gradient) of the line.
- \( c \) is the y-intercept (the value of \( y \) when \( x = 0 \)).

### Step 1: Identify the y-intercept
From the graph, the line crosses the y-axis at \( y = 4 \). So, \( c = 4 \).

### Step 2: Find the slope (\( m \))
The slope \( m \) is calculated using two points on the line. Let's pick two points:
- \( (0, 4) \) (where the line crosses the y-axis).
- \( (2, 0) \) (another point where the line crosses the x-axis).

The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the values:
\[
m = \frac{0 - 4}{2 - 0} = \frac{-4}{2} = -2
\]

### Step 3: Write the equation
Now that we have both \( m = -2 \) and \( c = 4 \), the equation of the line is:
\[
y = -2x + 4
\]

Would you like any further details or clarifications?

Here are 5 related questions you could explore:
1. How would the equation change if the slope were positive?
2. Can the equation be written in a different form, such as point-slope form?
3. What is the significance of the y-intercept in real-world applications?
4. How would the graph look if the y-intercept was negative?
5. How do you find the slope when the line is horizontal?

**Tip:** When calculating the slope, always use two distinct points on the line for the most accurate result.

Work out the equation of the straight line shown in the graph. Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.

Learn how to find the equation of a straight line using the slope and y-intercept. This example uses two points (0, 4) and (2, 0) to calculate the slope, then applies the equation y = mx + c to determine the final equation of the line. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation