Question

Find the equation and the y-intercept if the line passes through (20, 39) and has a slope of 2

y-intercept (b)=

Equation of the line:

Answer 1

To find the equation of a line given a point and the slope, we can use the point-slope form of the equation, which is:

\[
y - y_1 = m(x - x_1)
\]

where:
- \((x_1, y_1)\) is the given point,
- \(m\) is the slope.

Given:
- Point \((x_1, y_1) = (20, 39)\)
- Slope \(m = 2\)

Substituting these values into the point-slope form:

\[
y - 39 = 2(x - 20)
\]

Now, we can simplify this equation:

1. Distribute the slope:
\[
y - 39 = 2x - 40
\]

2. Add 39 to both sides to solve for \(y\):
\[
y = 2x - 40 + 39
\]
\[
y = 2x - 1
\]

Now we have the equation of the line:

**Equation of the line:**
\[
y = 2x - 1
\]

To find the y-intercept (\(b\)), we set \(x = 0\) in the equation:

\[
y = 2(0) - 1 = -1
\]

So, the y-intercept is:

**y-intercept (b) = -1**.

In summary:
- **Equation of the line:** \(y = 2x - 1\)
- **y-intercept (b):** -1