Question

a line passes through the points (3,0) and (4,1). what is the y intercept of the line

Answer 1

To find the y-intercept of the line that passes through the points (3, 0) and (4, 1), we first need to find the slope of the line.

The slope \( m \) can be calculated using the formula:

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

Substituting the coordinates of the points (3, 0) and (4, 1) into the formula:

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

Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:

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

Using the point (3, 0) and the slope \( m = 1 \):

\[
y - 0 = 1(x - 3)
\]

This simplifies to:

\[
y = x - 3
\]

To find the y-intercept, we need to evaluate the line equation when \( x = 0 \):

\[
y = 0 - 3 = -3
\]

Thus, the y-intercept of the line is \(-3\).