Question

What is the Standard Form of the line with x-intercept of 6 and y-intercept of 5?

6x + 5y = 30

5x + 6y = 11

5x + 6y = 30

6x + 5y = 11

Answer 1

To find the standard form of the line with an x-intercept of 6 and a y-intercept of 5, we first write the intercepts:

- The x-intercept (where y = 0) is 6, so the point is (6, 0).
- The y-intercept (where x = 0) is 5, so the point is (0, 5).

From these intercepts, we can find the equation of the line. The two points we have are (6, 0) and (0, 5).

We can use the slope-intercept form \(y = mx + b\), where m is the slope and b is the y-intercept. First, we find the slope \(m\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{0 - 6} = \frac{5}{-6} = -\frac{5}{6}
\]

Using the y-intercept (0, 5), we can write the equation in slope-intercept form:

\[
y = -\frac{5}{6}x + 5
\]

Next, we convert it into standard form \(Ax + By = C\):

1. Multiply every term by 6 to eliminate the fraction:

\[
6y = -5x + 30
\]

2. Rearrange it to get it into standard form:

\[
5x + 6y = 30
\]

Thus, the standard form of the line is:

\[
\boxed{5x + 6y = 30}
\]