/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 54 Find an equation of the line sat... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 54

Find an equation of the line satisfying the conditions. Write your answer in the slope-intercept form. Has \(x\) -intercept 3 and \(y\) -intercept \(-5\)

Short Answer

Expert verified
The equation of the line in slope-intercept form is \(y = \frac{5}{3}x - 5\).

Step by step solution

01

Find the slope (m)

To calculate the slope, we need to determine the change in y divided by the change in x using the x-intercept (3,0) and the y-intercept (0,-5). The change in y: \(\Delta y = -5 - 0 = -5\) The change in x: \( \Delta x = 0 - 3 = -3\) Slope (m): \(m = \frac{\Delta y}{\Delta x} = \frac{-5}{-3}\)
02

Simplify the slope (m)

We simplify the expression for the slope: \(m = \frac{-5}{-3} = \frac{5}{3}\) Now we have the slope, m = 5/3.
03

Write the equation in slope-intercept form (y = mx + b)

We know the slope is \(m = \frac{5}{3}\) and the y-intercept is -5. We can substitute these values into the slope-intercept form equation: \(y = \frac{5}{3}x - 5\) So, the equation of the line in slope-intercept form is: \(y = \frac{5}{3}x - 5\)

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Most popular questions from this chapter

Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=\sqrt{x}, \quad y=2 \sqrt{x-1}+1\)

Plot the graph of the function \(f\) in an appropriate viewing window. (Note: The answer is not unique.) $$ f(x)=\frac{\sin \sqrt{x}}{\sqrt{x}} $$

a. Plot the graph of \(f(x)=\cos (\sin x)\). Is \(f\) odd or even? b. Verify your answer to part (a) analytically.

Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=\sin x, \quad y=2 \sin \frac{x}{2}\)

Show that \(f\) and \(g\) are inverses of each other by verifying that \(f[g(x)]=x\) and \(g[f(x)]=x\). $$ f(x)=2 x+3 ; \quad g(x)=\frac{x-3}{2} $$
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