Questions: (-6,8))^(1/3)(4,-1) write equation in slope intercept form, using fractions when required

$(-6,8))^(1/3)(4,-1) write equation in slope intercept form, using fractions when required$

Transcript text: $(-6,8))^{\frac{1}{3}}(4,-1)$ write equation in slope intercept form, using fractions when required

Solution

Solution Steps

To write the equation in slope-intercept form (y = mx + b), we need to find the slope (m) using the two given points and then use one of the points to solve for the y-intercept (b).

Calculate the slope (m) using the formula: $ m = \frac{y_2 - y_1}{x_2 - x_1} $.
Use the slope and one of the points to solve for the y-intercept (b) using the equation: $ y = mx + b $.
Substitute the slope and y-intercept into the slope-intercept form.

Step 1: Calculate the Slope

To find the slope $ m $ between the points $ (-6, 8) $ and $ (4, -1) $, we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 8}{4 - (-6)} = \frac{-9}{10} = -0.9 \]

Step 2: Calculate the Y-Intercept

Next, we calculate the y-intercept $ b $ using the slope and one of the points, specifically $ (-6, 8) $:

\[ b = y_1 - m \cdot x_1 = 8 - (-0.9) \cdot (-6) = 8 - 5.4 = 2.6 \]

Step 3: Write the Equation in Slope-Intercept Form

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

\[ y = mx + b \implies y = -0.9x + 2.6 \]