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Chapter 2: Problem 62

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 passing through (-2, -7) that's parallel to the given line in point-slope form is \(y + 7 = -5(x + 2)\) and in slope-intercept form is \(y = -5x - 17\).

Step by step solution

01

Determine the slope from given equation

The given equation is \(y = -5x + 4\), which is in slope-intercept form. In this form, the coefficient of \(x\) is the slope. Here, the slope (\(m\)) of the given line is -5. Since parallel lines have identical slopes, the line passing through (-2, -7) will also have a slope of -5.
02

Use point-slope equation to write the new line

We have the point (-2, -7) and the slope. Substitute these values into the point-slope formula \(y - y_1 = m(x - x_1)\), we get \(y + 7 = -5(x + 2)\).
03

Convert to slope-intercept form

Multiplying out and simplifying Step 2 equation to the slope-intercept form \(y = mx + c\), we get \(y = -5x -10 -7\) -> \(y = -5x -17\). This is the line passing through (-2, -7) and parallel to \(y = -5x + 4\).

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