Questions: Write a slope-intercept equation for a line that passes through (5,0) and (-4,3) The slope-intercept equation for the line is

Solution Steps

To find the slope-intercept equation of a line that passes through 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 solve for the y-intercept (b) using the equation \( y = mx + b \).
3. Write the final equation in the form \( y = mx + b \).

To find the slope \( m \) of the line passing through the points \((5, 0)\) and \((-4, 3)\), we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points: \[ m = \frac{3 - 0}{-4 - 5} = \frac{3}{-9} = -0.3333 \]

Using the slope \( m \) and one of the points, we can find the y-intercept \( b \) using the equation \( y = mx + b \). Let's use the point \((5, 0)\): \[ 0 = (-0.3333)(5) + b \] \[ 0 = -1.6667 + b \] \[ b = 1.6667 \]

Now that we have the slope \( m \) and the y-intercept \( b \), we can write the equation of the line in slope-intercept form \( y = mx + b \): \[ y = -0.3333x + 1.6667 \]

Final Answer