Question

Q4 Emma rents an electric scooter to use for the day. She has to pay a deposit and a minute rate. Using the information from this graph, enter the values that complete the equation for this situation:
y = _____x + ______

the points on the graph are 4,17 and 1,8

Answer 1

To find the equation of the line represented by the points (4, 17) and (1, 8), we can use the point-slope form of a linear equation or find the slope and y-intercept directly.

1. **Calculate the slope (m)**:
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (1, 8) and (4, 17):
\[
m = \frac{17 - 8}{4 - 1} = \frac{9}{3} = 3
\]

2. **Use the slope to find the y-intercept (b)**:
We can use one of the points and the slope to find the y-intercept \( b \) using the equation:
\[
y = mx + b
\]
Using the point (1, 8):
\[
8 = 3(1) + b
\]
\[
8 = 3 + b
\]
\[
b = 8 - 3 = 5
\]

3. **Write the equation**:
Now, substituting the slope and y-intercept into the y = mx + b format, we get:
\[
y = 3x + 5
\]

Thus, the completed equation is:
\[
y = 3x + 5
\]

Therefore, the answer is:
**3** and **5**.