Question

(0,1) and (1,4) are plotted on the graph.
What is slope and y-intercept

Write equation in slope-intercept form:

Answer 1

To find the slope and y-intercept of the line that passes through the points (0, 1) and (1, 4), we can use the slope formula and the point-slope form of the equation.

1. **Calculate the slope (m)**:
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

For the points (0, 1) and (1, 4):
- \((x_1, y_1) = (0, 1)\)
- \((x_2, y_2) = (1, 4)\)

Plugging in these values:

\[
m = \frac{4 - 1}{1 - 0} = \frac{3}{1} = 3
\]

2. **Find the y-intercept (b)**:
The y-intercept is the value of \( y \) when \( x = 0 \). From the point (0, 1), we can see that the y-intercept is 1.

3. **Write the equation in slope-intercept form**:
The slope-intercept form of a line is given by:

\[
y = mx + b
\]

Substituting the slope \( m = 3 \) and y-intercept \( b = 1 \):

\[
y = 3x + 1
\]

So, the slope is 3, the y-intercept is 1, and the equation in slope-intercept form is:

\[
y = 3x + 1
\]