Questions: Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through (-4,-7) and (1,3) What is the equation of the line in point-slope form? (Simplify your answer. Use integers or fractions for any numbers in the equation.)

$Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through (-4,-7) and (1,3) What is the equation of the line in point-slope form? (Simplify your answer. Use integers or fractions for any numbers in the equation.)$

Transcript text: Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through $(-4,-7)$ and $(1,3)$ What is the equation of the line in point-slope form? $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Solution

Solution Steps

To find the equation of the line passing through two points, we need to:

Calculate the slope (m) using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $.
Use the point-slope form of the equation of a line, which is $ y - y_1 = m(x - x_1) $.

Step 1: Calculate the Slope

Given points $(-4, -7)$ and $ (1, 3) $, we calculate the slope $ m $ using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points: \[ m = \frac{3 - (-7)}{1 - (-4)} = \frac{3 + 7}{1 + 4} = \frac{10}{5} = 2 \]

Step 2: Write the Point-Slope Form

Using the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Substituting $ m = 2 $ and the point $(-4, -7)$: \[ y - (-7) = 2(x - (-4)) \] Simplifying: \[ y + 7 = 2(x + 4) \]