Questions: Find the equation of the line in slope-intercept form that passes through the point (-4,4) and (1,-6). Equation of line:

Solution Steps

To find the equation of a line in slope-intercept form (y = mx + b) that passes through two given points, we first calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Then, we use one of the points and the slope to solve for the y-intercept (b) using the equation \( y = mx + b \).

To find the slope \( m \) of the line passing through the points \((-4, 4)\) and \((1, -6)\), we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 4}{1 - (-4)} = \frac{-10}{5} = -2.0 \]

Next, we use the slope \( m \) and one of the points, say \((-4, 4)\), to find the y-intercept \( b \) using the equation:

\[ y = mx + b \implies b = y - mx \]

Substituting the values:

\[ b = 4 - (-2.0)(-4) = 4 - 8 = -4.0 \]

Now that we have both the slope and the y-intercept, we can write the equation of the line in slope-intercept form:

\[ y = mx + b \implies y = -2.0x - 4.0 \]

Final Answer