Problem 50 - Introductory and Intermediate Algebra for College Students 4th

Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-7)\) and parallel to the line whose equation is \(y=-5 x+4\)

Step-by-Step Solution

Answer

The equation of the line passing through (-2,-7) and parallel to the line whose equation is \(y=-5x+4\), in point-slope form is \(y + 7 = -5(x + 2)\) and in slope-intercept form is \(y = -5x - 17\).

Step 1: Identify the slope of the given line

From the equation \(y=-5x+4\), it's clear that the slope of the given line is -5. Since parallel lines have the same slope, the slope of the required line will be -5.

Step 2: Use point-slope form

The point-slope form is \(y - y_1 = m(x - x_1)\) where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line. Substituting \((x_1, y_1) = (-2,-7)\) and \(m = -5\) into the formula, gives the equation \(y - (-7) = -5(x -(-2))\), which simplifies to \(y + 7 = -5(x + 2)\).

Step 3: Convert to slope-intercept form

To convert point-slope form to slope intercept form, expand then simplify in the format \(y = mx + b\). Expanding gives \(y + 7 = -5x - 10\). Simplify to obtain \(y = -5x - 17\).