Questions: Find an equation of the line that passes through the two given points. If possible, write the equation in slope-intercept form. Check that the graph of the equation contains the given points. (-4,-20) and (6,20)

Solution Steps

To find the equation of the line that passes through the two given points, we need to:

1. Calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Use the slope and one of the points to find the y-intercept (b) using the formula \( y = mx + b \).
3. Write the equation in slope-intercept form \( y = mx + b \).
4. Verify that the equation contains the given points by substituting the points into the equation.

Given points \((-4, -20)\) and \( (6, 20) \), we calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points: \[ m = \frac{20 - (-20)}{6 - (-4)} = \frac{40}{10} = 4.0 \]

Using the slope \( m = 4.0 \) and one of the points, say \((-4, -20)\), we find the y-intercept \( b \) using the formula: \[ y = mx + b \] Substituting the values: \[ -20 = 4.0 \cdot (-4) + b \implies -20 = -16 + b \implies b = -4.0 \]

Using the calculated slope \( m = 4.0 \) and y-intercept \( b = -4.0 \), the equation of the line is: \[ y = 4.0x - 4.0 \]

We verify that the equation \( y = 4.0x - 4.0 \) contains the given points:

• For \((-4, -20)\): \[ y = 4.0(-4) - 4.0 = -16 - 4 = -20 \quad \text{(True)} \]
• For \( (6, 20) \): \[ y = 4.0(6) - 4.0 = 24 - 4 = 20 \quad \text{(True)} \]

Final Answer