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Chapter 4: Problem 2

How do you put an equation that is in standard form, \(A x+B y=C,\) into slope- intercept form?

Short Answer

Expert verified
To convert an equation in standard form, \(Ax + By = C\), into slope-intercept form, \(y = mx + b\), first solve for y in terms of x by subtracting Ax from both sides and then dividing by B: \(y = \frac{-A}{B}x + \frac{C}{B}\). The slope (m) is \(\frac{-A}{B}\) and the y-intercept (b) is \(\frac{C}{B}\).

Step by step solution

01

Write down the standard form equation

Given the equation: \(Ax + By = C\)
02

Solve for y in terms of x

To get the equation in slope-intercept form, we need it to look like y = mx + b. So, let's isolate y: Subtract Ax from both sides of the equation: \(By = -Ax + C\) Now, we need to get rid of the B (the coefficient of y). To do this, divide both sides of the equation by B: \[\frac{By}{B} = \frac{-Ax + C}{B}\] Which simplifies to: \(y = \frac{-A}{B}x + \frac{C}{B}\)
03

Identify the slope and y-intercept

Now the equation is in slope-intercept form, which is (y = mx + b), we can identify the slope (m) and y-intercept (b): Slope (m) = \(\frac{-A}{B}\) Y-intercept (b) = \(\frac{C}{B}\) In conclusion, to convert an equation in standard form (Ax + By = C) into slope-intercept form (y = mx + b), we must first isolate y in terms of x, and then identify the slope (m) and y-intercept (b) from the resulting equation.

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Most popular questions from this chapter

Graph each function using the slope and \(y\) -intercept. $$g(x)=3 x+3$$

Graph each function by making a table of values and plotting points. $$f(x)=x+2$$

Lines \(L_{1}\) and \(L_{2}\) contain the given points. Determine if lines \(L_{1}\) and \(L_{2}\) are parallel, perpendicular, or neither. $$\begin{aligned}&L_{1}:(5,-1),(7,3)\\\&L_{2}:(-6,0),(4,5)\end{aligned}$$

Write an equation of the line parallel to the given line and containing the given point. Write the answer in slope intercept form or in standard form, as indicated. \(x+5 y=10 ;(15,7) ;\) slope-intercept form

Determine the domain of each relation, and determine whether each relation describes \(y\) as a function of \(x .\) $$y=\frac{6}{5 x-3}$$
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