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Chapter 1: Problem 27

Find an equation of the line that passes through the point and has the indicated slope \(m\). $$ (3,-4) ; m=2 $$

Short Answer

Expert verified
The equation of the line that passes through the point (3, -4) and has a slope of 2 is \(y = 2x - 10\).

Step by step solution

01

Identify the given point and slope

We are given a point \((3, -4)\) and the slope \(m = 2\). We'll use these values to find the equation of the line.
02

Plug in the values into the point-slope form

Now, we'll plug in the values of \(x_1\), \(y_1\) and \(m\) into the point-slope form equation: $$ y - (-4) = 2(x - 3) $$
03

Simplify the equation

First, simplify the equation by removing the double negative sign in front of \(y\): $$ y + 4 = 2(x - 3) $$ Next, distribute the slope on the right side of the equation: $$ y + 4 = 2x - 6 $$
04

Solve for y

Subtract 4 from both sides of the equation to isolate \(y\): $$ y = 2x - 6 - 4 $$ Simplify the equation: $$ y = 2x - 10 $$
05

Write the final equation

Now that we have solved for \(y\), the equation of the line that passes through the point (3, -4) and has a slope of 2 is: $$ y = 2x - 10 $$

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Most popular questions from this chapter

The demand equation for the Schmidt- 3000 fax machine is \(3 x+p-1500=0\), where \(x\) is the quantity demanded per week and \(p\) is the unit price in dollars. The supply equation is \(2 x-3 p+1200=\) 0\. where \(x\) is the quantity the supplier will make available in the market each week when the unit price is \(p\) dollars. Find the equilibrium quantity and the equilibrium price for the fax machines.

The demand equation for the Sicard wristwatch is $$ p=-0.025 x+50 $$ where \(x\) is the quantity demanded per week and \(p\) is the unit price in dollars. Sketch the graph of the demand equation. What is the highest price (theoretically) anyone would pay for the watch?

Find an equation of the line that has slope \(m\) and \(y\) -intercept \(b\). $$ m=-\frac{1}{2} ; b=\frac{3}{4} $$

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