Questions: Write an equation of the line passing through the points (5,-31) and (-4,14). The equation of the line is □ (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers the equation.)

Solution Steps

To find the equation of the line passing through two 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 point-slope form of the equation \( y - y_1 = m(x - x_1) \) to find the equation.
3. Simplify the equation to slope-intercept form \( y = mx + b \).

To find the slope \( m \) of the line passing through the points \( (5, -31) \) and \( (-4, 14) \), we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - (-31)}{-4 - 5} = \frac{14 + 31}{-9} = \frac{45}{-9} = -5.0 \]

Next, we use the point-slope form of the equation to find the y-intercept \( b \). We can use one of the points, say \( (5, -31) \): \[ b = y_1 - m \cdot x_1 = -31 - (-5.0) \cdot 5 = -31 + 25 = -6.0 \]

Now that we have both the slope and the y-intercept, we can write the equation of the line in slope-intercept form: \[ y = mx + b = -5.0x - 6.0 \]

Final Answer