Question

Find an equation
​x-intercept: negative 7
​y-intercept: 2

Answer 1

To find the equation of a line given the x-intercept and y-intercept, we can use the intercept form of the linear equation:

\[
\frac{x}{a} + \frac{y}{b} = 1
\]

where \(a\) is the x-intercept and \(b\) is the y-intercept.

In this case:
- The x-intercept \(a\) is \(-7\).
- The y-intercept \(b\) is \(2\).

Substituting these values into the formula gives:

\[
\frac{x}{-7} + \frac{y}{2} = 1
\]

To get rid of the denominators, we can multiply the entire equation by \(-14\) (which is the least common multiple of the denominators):

\[
-14 \left(\frac{x}{-7}\right) + -14 \left(\frac{y}{2}\right) = -14 \cdot 1
\]

This simplifies to:

\[
2x - 7y = -14
\]

Now, we can rearrange this into slope-intercept form \(y = mx + b\) if desired (though it isn't necessary):

1. Rearranging gives:
\[
7y = 2x + 14
\]
2. Dividing everything by \(7\) gives:
\[
y = \frac{2}{7}x + 2
\]

Thus, the equation of the line with the given x-intercept and y-intercept is:

\[
2x - 7y = -14
\]

or in slope-intercept form:

\[
y = \frac{2}{7}x + 2
\]