Question

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

y-intercept (b)=

Answer 1

To find the equation of the line that passes through the point \((20, 39)\) with a slope of \(m = 2\), we can use the point-slope form of the equation of a line, which is:

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

where \((x_1, y_1)\) is the point the line passes through, and \(m\) is the slope of the line. Plugging in the values:

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

Next, we can simplify this equation:

\[
y - 39 = 2x - 40
\]

Adding 39 to both sides gives:

\[
y = 2x - 1
\]

This is the equation of the line in slope-intercept form \(y = mx + b\).

To find the y-intercept (\(b\)), we can observe from the equation that:

\[
b = -1
\]

Therefore, the y-intercept is:

\[
\text{y-intercept } (b) = -1
\]

So the final answer is:

**Equation:** \(y = 2x - 1\)

**y-intercept:** \(b = -1\)