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:
- Line M: \( y = -2x + 4 \)
- Line N: \( y = -3x + 3 \)