Question

What is an equation in standard form of the line that has x-intercept 1 and y-intercept 4?

Answer 1

To find the equation of a line in standard form \(Ax + By = C\) given the x-intercept and y-intercept, we can start from the intercepts.

The x-intercept is the point where the line crosses the x-axis, which is (1, 0). The y-intercept is the point where the line crosses the y-axis, which is (0, 4).

Using these two points, we can first find the slope \(m\) of the line:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 0}{0 - 1} = \frac{4}{-1} = -4.
\]

Now we can use the point-slope form of the line equation \(y - y_1 = m(x - x_1)\). We can use the y-intercept (0, 4):

\[
y - 4 = -4(x - 0).
\]

This simplifies to:

\[
y - 4 = -4x,
\]
\[
y = -4x + 4.
\]

Next, we need to convert this equation into standard form \(Ax + By = C\). We can rearrange the equation as follows:

\[
4x + y = 4.
\]

Thus, the equation of the line in standard form is:

\[
4x + y = 4.
\]