Exercise 33 Page 180

We want to write the slope-intercept form for Ax+By=C. Then, we want to use this answer to find the slope and y-intercept of the graph of the equation - 6x+5y=9.

Writing Ax+By=C in Slope-intercept Form

To write Ax+By=C in slope-intercept form we have to isolate the y-variable. To do so we need to assume that B≠ 0, since division by zero is not defined.

Ax+By=C

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Write in slope-intercept form

SubEqn

LHS-Ax=RHS-Ax

By=- Ax+C

DivEqn

.LHS /B.=.RHS /B.

y=- Ax+C/B

WriteSumFrac

Write as a sum of fractions

y=- A/Bx +C/B

MoveNegNumToFrac

Put minus sign in front of fraction

y=- A/Bx +C/B

We found the slope-intercept form of the given line.

Slope-Intercept Form:& y = - A/Bx + C/B, B≠ 0

Finding the Slope and y-intercept of - 6x+5y=9

Let's compare the equations of a line when it is written in standard form and when it is written in slope-intercept form. Standard Form:& Ax+ By= C Slope-Intercept Form:& y = - A/Bx + C/B, B≠ 0 In the second of the above equations, the slope of the line is - A B and the y-intercept is C B. Note that the given equation is written in standard form. Let's identify the values of A, B, and C. - 6x+ 5y= 9 We see that A= - 6, B= 5, and C= 9. By substituting these values into the expressions - AB and CB, we can determine the slope and the y-intercept of the line. Let's start with the slope.

Slope=- A/B

SubstituteII

A= -6, B= 5

Slope=- - 6/5

RemoveNegFracAndNum

- - a/b= a/b

Slope=6/5

The slope of the line is 65. Let's now substitute 9 for C and 5 for B in C B to obtain the y-intercept.

y-intercept=C/B

SubstituteII

C= 9, B= 5

y-intercept=9/5