Question

for the equation shown below, the slope =
and the y-intercept is the
point ( , ).
$y + 12 = 2x - 35$
question 6
6 pts
for the equation shown below, the slope =
and the y-intercept is the
point ( , ).
$-2y = -2x + 14$

Explanation:

Step1: Rewrite first equation to slope-intercept form

Subtract 12 from both sides:
$y + 12 - 12 = 2x - 35 - 12$
Simplify to get: $y = 2x - 47$

Step2: Identify slope and y-intercept (1st eq)

Slope is coefficient of $x$: $m=2$. Y-intercept occurs at $x=0$, so $y=2(0)-47=-47$, giving the point $(0, -47)$.

Step3: Rewrite second equation to slope-intercept form

Divide all terms by $-2$:
$\frac{-2y}{-2} = \frac{-2x}{-2} + \frac{14}{-2}$
Simplify to get: $y = x - 7$

Step4: Identify slope and y-intercept (2nd eq)

Slope is coefficient of $x$: $m=1$. Y-intercept occurs at $x=0$, so $y=0-7=-7$, giving the point $(0, -7)$.

Answer:

For equation $y + 12 = 2x - 35$:

Slope = $2$, y-intercept point = $(0, -47)$

For equation $-2y = -2x + 14$:

Slope = $1$, y-intercept point = $(0, -7)$