Question

use slope-intercept form to write an equation of a line passing through the given point and having the given slope. express the answer in standard form.

(p(-4, -5); m = -\frac{3}{4})

Explanation:

Identify given values and forms

We are given:

• Point \(P(x_1, y_1) = (-4, -5)\)
• Slope \(m = -\frac{3}{4}\)

We need to:

1. Use slope-intercept form: \(y = mx + b\)
2. Convert to standard form: \(Ax + By = C\) (where \(A, B, C\) are integers, and usually \(A \ge 0\))

Find the y-intercept

Substitute the slope \(m = -\frac{3}{4}\) and point \((-4, -5)\) into the slope-intercept equation:

$$ y = mx + b $$

$$ -5 = -\frac{3}{4}(-4) + b $$

$$ -5 = 3 + b $$

$$ b = -8 $$

Write in slope-intercept form

Substitute \(m\) and \(b\) back into the slope-intercept equation:

$$ y = -\frac{3}{4}x - 8 $$

Convert to standard form

Multiply the entire equation by 4 to clear the fraction:

$$ 4y = -3x - 32 $$

Add \(3x\) to both sides to group variables on the left:

$$ 3x + 4y = -32 $$

Answer:

Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the answer in standard form.

\(P(-4, -5); m = -\frac{3}{4}\)

<blank>\(3x + 4y = -32\)</blank>