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Chapter 2: Problem 10

Use the given conditions to write an equation for each line in point-slope form and general form. Passing through \((-1,3)\) and parallel to the line whose equation is \(3 x-2 y-5=0\)

Short Answer

Expert verified
The point-slope form of the line is \(y - 3 = 1.5(x + 1)\) and the general form is \(-1.5x + y - 4.5 = 0\).

Step by step solution

01

Extract Slope From Given Line

The equation of the give line is in the standard form Ax + By + C = 0. Convert it into slope-intercept form to find the slope. The slope-intercept form is y = mx + c where m is the slope. Thus we can re-arrange the given equation as follows: \(2y = 3x - 5\) or \(y = 1.5x - 2.5\). The slope of this line is 1.5.
02

Understand the Concept of Parallel Lines

Parallel lines have the same slope. Therefore, the new line that is parallel to the given line will also have a slope of 1.5.
03

Incorporate Point in the Equation

Use the point-slope form of line equation which is (y - y1) = m(x - x1) where (x1, y1) is the point the line passes through and m is the slope. Our line therefore is \(y - 3 = 1.5(x - (-1))\), simplifying to \(y - 3 = 1.5x + 1.5\).
04

Simplify Equation to General Form

Subtract 1.5x from both sides to get it into the general form Ax + By + C = 0. The equation, when simplified, becomes \(-1.5x + y - 4.5 = 0\).

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Most popular questions from this chapter

The bar graph shows your chances of surviving to various ages once you reach 60 The functions $$ \begin{aligned} f(x) &=-2.9 x+286 \\ \text { and } g(x) &=0.01 x^{2}-4.9 x+370 \end{aligned} $$ model the chance, as a percent, that a 60 -year-old will survive to age \(x .\) Use this information to solve Exercises \(101-102\) a. Find and interpret \(f(90)\) b. Find and interpret \(g(90)\) c. Which function serves as a better model for the chance of surviving to age \(90 ?\)

In your own words, describe how to find the distance between two points in the rectangular coordinate system.

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complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}+3 x+5 y+\frac{9}{4}=0 $$

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}+8 x+4 y+16=0 $$
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