Question

the graph of a system of equations has these characteristics: line M has an x-intercept of 2 and a y-intercept of 4. line n has an x-intercept of 1 and a y-intercept of 3.
what is the system of equations, written in slope-intercept form, that represents the lines?

Answer 1

To write the equations of the lines in slope-intercept form (y = mx + b), we first need to determine the slope (m) of each line using the given intercepts.

### Line M
- **x-intercept**: 2 (this means the point is (2, 0))
- **y-intercept**: 4 (this means the point is (0, 4))

We can calculate the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Taking the points (2, 0) and (0, 4):

\[
m = \frac{4 - 0}{0 - 2} = \frac{4}{-2} = -2
\]

Now, we can use the slope and the y-intercept to write the equation of line M:
\[
y = -2x + 4
\]

### Line N
- **x-intercept**: 1 (this means the point is (1, 0))
- **y-intercept**: 3 (this means the point is (0, 3))

Using the same slope formula with points (1, 0) and (0, 3):

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

Now we write the equation of line N:
\[
y = -3x + 3
\]

### Final System of Equations
The system of equations, in slope-intercept form, is:
1. Line M: \( y = -2x + 4 \)
2. Line N: \( y = -3x + 3 \)