Questions: QUESTION 13 Find the equation of a line using the information below. Write your final answer in slope-intercept form. Passing through (-5,4) with slope -3 . a) y=-3 x+17 b) y=-3 x-1 c) y=-3 x+4 d) y=-3 x-11

QUESTION 13 Find the equation of a line using the information below. Write your final answer in slope-intercept form. Passing through (-5,4) with slope -3 . a) y=-3 x+17 b) y=-3 x-1 c) y=-3 x+4 d) y=-3 x-11
Transcript text: QUESTION 13 Find the equation of a line using the information below. Write your final answer in slope-intercept form. Passing through $(-5,4)$ with slope -3 . a) $y=-3 x+17$ b) $y=-3 x-1$ c) $y=-3 x+4$ d) $y=-3 x-11$ A B C D
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Solution

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Solution Steps

To find the equation of a line in slope-intercept form \( y = mx + b \) given a point \((x_1, y_1)\) and a slope \( m \), we can use the point-slope form of the equation \( y - y_1 = m(x - x_1) \) and then convert it to slope-intercept form.

  1. Start with the point-slope form: \( y - 4 = -3(x + 5) \).
  2. Simplify and solve for \( y \) to get it into slope-intercept form.
Step 1: Identify the Given Information

We are given a point \((-5, 4)\) and a slope \( m = -3 \).

Step 2: Use the Point-Slope Form

The point-slope form of the equation of a line is: \[ y - y_1 = m(x - x_1) \] Substituting the given point and slope: \[ y - 4 = -3(x + 5) \]

Step 3: Simplify to Slope-Intercept Form

Expand and simplify the equation to get it into slope-intercept form \( y = mx + b \): \[ y - 4 = -3x - 15 \] \[ y = -3x - 15 + 4 \] \[ y = -3x - 11 \]

Final Answer

\(\boxed{y = -3x - 11}\)

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