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Chapter 1: Problem 61

Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ y+5=0 $$

Short Answer

Expert verified
The given linear equation is \(y + 5 = 0\), which can be rewritten as \(y = -5\). This represents a horizontal line that does not intersect the x-axis (no x-intercept) and intersects the y-axis at the point (0, -5). So, the line can be sketched as a horizontal line passing through the point (0, -5).

Step by step solution

01

Write the given equation in slope-intercept form.

The given equation is y + 5 = 0. We can rewrite this in slope-intercept form (y = mx + b) by isolating y on one side of the equation: $$ y = -5 $$ In this form, the equation represents a horizontal line with a y-intercept of -5.
02

Find the x-intercept.

The x-intercept is the point where the line crosses the x-axis. At this point, the y-coordinate is 0. We plug in y = 0 into our equation and solve for x: $$ 0 = -5 $$ This equation is not true, which indicates that the line does not intersect the x-axis. There is no x-intercept.
03

Find the y-intercept.

The y-intercept is the point where the line crosses the y-axis. At this point, the x-coordinate is 0. Since we already have the equation in the form y = -5, we know it intersects the y-axis at y = -5. So, the y-intercept of the line is the point (0, -5).
04

Sketch the straight line.

We now have all the information needed to sketch the straight line: 1. There is no x-intercept. 2. The y-intercept is at the point (0, -5). Based on this information, we can sketch a horizontal line passing through the y-axis at the point (0, -5) that continues in both directions along the line y = -5. This will be our final sketch of the straight line defined by the given equation.

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Most popular questions from this chapter

Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ x+2 y-4=0 $$

The number of U.S. broadband Internet households (in millions) between the beginning of \(2004(t=0)\) and the beginning of \(2008(t=4)\) was estimated to be $$ f(t)=6.5 t+33 \quad(0 \leq t \leq 4) $$ Over the same period, the number of U.S. dial-up Internet households (in millions) was estimated to be $$ g(t)=-3.9 t+42.5 \quad(0 \leq t \leq 4) $$ a. Sketch the graphs of \(f\) and \(g\) on the same set of axes. b. Solve the equation \(f(t)=g(t)\) and interpret your result.

Use the results of Exercise 63 to find an equation of a line with the \(x\) - and \(y\) -intercepts. $$ x \text { -intercept }-\frac{1}{2} ; y \text { -intercept } \frac{3}{4} $$

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

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.
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