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Chapter 2: Problem 6

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 \(y=-5 x+4\)

Short Answer

Expert verified
The equation of the line in point-slope form is \(y + 7 = -5(x + 2)\) which simplifies to \(y = -5x - 17\) in slope-intercept form.

Step by step solution

01

Identify the slope of the line

Parallel lines have the same slope. If the given line is \(y = -5x + 4\), the slope (m) of that line is -5. Therefore, the slope of the line parallel to this is also -5.
02

Use the point-slope form to write equation of the line

The point-slope form of the linear equation is \(y - y_1 = m(x - x_1)\). Plugging in the given point (-2, -7), into (x_1, y_1) and the slope as -5, the equation becomes \(y - (-7) = -5(x - (-2))\), which simplifies to \(y + 7 = -5(x + 2)\). After rearranging, we get \(y = -5x - 10 - 7\) or \(y = -5x - 17\).
03

Write the equation in slope-intercept form

The slope-intercept form of an equation is \(y = mx + b\). We already have this form as \(y = -5x - 17\), where m = -5 is the slope and b = -17 is the y-intercept.

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