Question

wednesday
write an equation of the line in slope - intercept form.
$2x + 3y = 6$
write an equation of the line in point - slope form.
$(8,3)$ slope: 1
write the equation in standard form and identify a, b, and c.
$y = 4x - 2$
graph $y = - 4$

thursday
write an equation of the line in slope - intercept form.
$3x - y = 12$
write an equation of the line in point - slope form.
$(-6,7)$ slope: 0
write the equation in standard form and identify a, b, and c.
$y=\frac{1}{3}x + 1$
graph $x = - 3$

friday
write an equation of the line in slope - intercept form.
slope: - 3 and y - intercept: 2
$x - 2y = - 5$
write an equation of the line in point - slope form.
$(4,9)$ slope: 5
write the equation in standard form and identify a, b, and c.
$y = - 2x + 3$
graph $y = - 2x + 3$

Explanation:

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WEDNESDAY

Problem 1: Slope-intercept form

Step1: Isolate $3y$

$3y = -2x + 6$

Step2: Solve for $y$

$y = \frac{-2x + 6}{3} = -\frac{2}{3}x + 2$

Problem 2: Point-slope form

Step1: Use point-slope formula

Point-slope form: $y - y_1 = m(x - x_1)$
Substitute $(x_1,y_1)=(8,3), m=1$
$y - 3 = 1(x - 8)$

Problem 3: Standard form

Step1: Rearrange to standard form

Standard form: $Ax + By = C$
$y = 4x - 2 \implies -4x + y = -2$
Multiply by -1: $4x - y = 2$
Identify $A=4, B=-1, C=2$

Problem 4: Graph $y=-4$

Step1: Identify line type

Horizontal line at $y=-4$, passes through all points where $y=-4$ (e.g., $(-2,-4), (3,-4)$)

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THURSDAY

Problem 1: Slope-intercept form

Step1: Isolate $-y$

$-y = -3x + 12$

Step2: Solve for $y$

$y = 3x - 12$

Problem 2: Point-slope form

Step1: Use point-slope formula

Substitute $(x_1,y_1)=(-6,7), m=0$
$y - 7 = 0(x + 6)$

Problem 3: Standard form

Step1: Eliminate fraction, rearrange

$y = \frac{1}{3}x + 1 \implies 3y = x + 3 \implies -x + 3y = 3$
Multiply by -1: $x - 3y = -3$
Identify $A=1, B=-3, C=-3$

Problem 4: Graph $x=-3$

Step1: Identify line type

Vertical line at $x=-3$, passes through all points where $x=-3$ (e.g., $(-3,2), (-3,-4)$)

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FRIDAY

Problem 1: Slope-intercept form

Step1: Use slope-intercept formula

Slope-intercept form: $y = mx + b$
Substitute $m=-3, b=2$: $y = -3x + 2$

Step2: Convert $x-2y=-5$ to slope-intercept

Isolate $-2y$: $-2y = -x -5$
Solve for $y$: $y = \frac{1}{2}x + \frac{5}{2}$

Problem 2: Point-slope form

Step1: Use point-slope formula

Substitute $(x_1,y_1)=(4,9), m=5$
$y - 9 = 5(x - 4)$

Problem 3: Standard form

Step1: Rearrange to standard form

$y = -2x + 3 \implies 2x + y = 3$
Identify $A=2, B=1, C=3$

Problem 4: Graph $y=-2x+3$

Step1: Identify intercepts

y-intercept: $(0,3)$; x-intercept: set $y=0$: $0=-2x+3 \implies x=\frac{3}{2}$, so $(\frac{3}{2},0)$
Plot intercepts and draw line through them.

Answer:

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WEDNESDAY

1. $y = -\frac{2}{3}x + 2$
2. $y - 3 = x - 8$
3. Standard form: $4x - y = 2$; $A=4$, $B=-1$, $C=2$
4. Horizontal line through $y=-4$

THURSDAY

1. $y = 3x - 12$
2. $y - 7 = 0$
3. Standard form: $x - 3y = -3$; $A=1$, $B=-3$, $C=-3$
4. Vertical line through $x=-3$

FRIDAY

1. $y = -3x + 2$; $y = \frac{1}{2}x + \frac{5}{2}$
2. $y - 9 = 5(x - 4)$
3. Standard form: $2x + y = 3$; $A=2$, $B=1$, $C=3$
4. Line through $(0,3)$ and $(\frac{3}{2}, 0)$