https://file.aiquickdraw.com/mathbot/file/1728242093632lg8u8oyt.jpg

To determine the equation of the straight line shown, we need to find its **slope** \( m \) and **y-intercept** \( c \).

1. **Identifying two points on the line:**
   From the graph, two clear points on the line are:
   - Point 1: \( (0, 4) \) (this is the y-intercept)
   - Point 2: \( (4, 16) \)

2. **Finding the slope \( m \):**
   The formula for the slope is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the coordinates of the two points \( (0, 4) \) and \( (4, 16) \):
   \[
   m = \frac{16 - 4}{4 - 0} = \frac{12}{4} = 3
   \]

3. **Finding the y-intercept \( c \):**
   The y-intercept is the value of \( y \) when \( x = 0 \). From the graph, we can see that the line crosses the y-axis at \( (0, 4) \), so \( c = 4 \).

4. **Equation of the line:**
   Using the slope-intercept form \( y = mx + c \), where \( m = 3 \) and \( c = 4 \), the equation of the line is:
   \[
   y = 3x + 4
   \]

Would you like further clarification or more details on this? 

Here are some related questions to explore:
1. How do you calculate the slope if the two points are not clearly defined on a graph?
2. What would the equation look like if the slope were negative?
3. How does the y-intercept affect the position of the line on the graph?
4. Can you derive the equation from just the slope and one point on the line?
5. How would you find the equation if the points involved fractions?

**Tip:** When finding the slope of a line, ensure you clearly identify two points on the graph to avoid calculation errors.

What is the equation of the straight line shown below? 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 from a graph using two points and the slope-intercept form. This problem covers key algebraic concepts such as calculating the slope and identifying the y-intercept. Suitable 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