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.

Question

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: \( y = -3x + 3 \)