Question

objective: swbat write an equation in slope intercept form given the slopedirections: answer the following questions. star any questions that you are unsure of!1. without graphing, write the slope-intercept form of the equation for each line described below.a. the line that passes through point $(-2, 6)$ and has a slope of -12.b. the line that passes through point $(-4, -6)$ and has a slope of 3.2. in order to become a member at a local gym, there is a $20 fee every month. sandra has gone to the gym for two months so far and has paid $90. write an equation that could be used to determine the cost of the gym membership for $x$ months.3. a line with a slope of -6 passes through point $(-2, 4)$. what is the equation for this line?

Explanation:

Step1: Use point-slope form for 1a

Point-slope form: $y - y_1 = m(x - x_1)$
Substitute $m=-12$, $x_1=-2$, $y_1=6$:
$y - 6 = -12(x - (-2))$

Step2: Simplify to slope-intercept for 1a

Expand and solve for $y$:
$y - 6 = -12x - 24$
$y = -12x - 24 + 6$
$y = -12x - 18$

Step3: Use point-slope form for 1b

Substitute $m=3$, $x_1=-4$, $y_1=-6$:
$y - (-6) = 3(x - (-4))$

Step4: Simplify to slope-intercept for 1b

Expand and solve for $y$:
$y + 6 = 3x + 12$
$y = 3x + 12 - 6$
$y = 3x + 6$

Step5: Find initial fee for question 2

Let $C = mx + b$, $m=20$, $x=2$, $C=90$:
$90 = 20(2) + b$
$90 = 40 + b$
$b = 90 - 40 = 50$
Equation: $C = 20x + 50$

Step6: Use point-slope form for question 3

Substitute $m=-6$, $x_1=-2$, $y_1=4$:
$y - 4 = -6(x - (-2))$

Step7: Simplify to slope-intercept for question3

Expand and solve for $y$:
$y - 4 = -6x - 12$
$y = -6x - 12 + 4$
$y = -6x - 8$

Answer:

1a. $y = -12x - 18$
1b. $y = 3x + 6$

1. $C = 20x + 50$ (where $C$ is total cost)
2. $y = -6x - 8$