Objective 2 - Converting between linear forms

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Converting between Slope-Intercept form and Standard form.

Link to section in online textbook and link to section in Prelude to Active Calculus textbook.

First, watch the video below to learn about the different forms we usually write linear functions in. You can use the notes here to follow along with the video and record your thoughts.

Convert the linear function below from Standard form to Slope-Intercept form.

$\sage {equationXY1} = \sage {C1}$

$y = \answer [tolerance=0.05]{\sage {slope1}}x + \answer [tolerance=0.05]{\sage {yInt1}}$

Convert the linear function below from Standard form to Slope-Intercept form.

$\sage {equationXY2} = \sage {C2}$

$y = \answer [tolerance=0.05]{\sage {slope2}}x + \answer [tolerance=0.5]{\sage {yInt2}}$

Convert the linear function below from Slope-Intercept form to Standard form.

$y = \sage {equationSlopeInt3}$

What do we know about the coefficients in Standard Form? Is there anything special about the coefficient for $x$ ?

$\answer {\sage {A3}}x + \answer {\sage {B3}}y = \answer {\sage {C3}}$

Convert the linear function below from Slope-Intercept form to Standard form.

$y = \sage {equationSlopeInt4}$

What do we know about the coefficients in Standard Form? Is there anything special about the coefficient for $x$ ?

$\answer {\sage {A4}}x + \answer {\sage {B4}}y = \answer {\sage {C4}}$

Press...	...to do
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ctrl+x/c/v	Cut/copy/paste
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ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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