Question

crm 1.2 test: two - variable linear equations
test id: 3701579

1. which equation shows 8x - 12y = 48 rewritten in slope - intercept form?

a. 2x - 3y = 12
b. y = - 8x + 60
c. x = \frac{3}{2}y + 6
d. y = \frac{2}{3}x - 4

1. an equation is shown: y - 3 = 4(x - 2)

choose from the given values to write the equation in standard form:
\

$$\begin{bmatrix}-5\\-4\\4\\1\\end{bmatrix}$$

x+\

$$\begin{bmatrix}5\\1\\-4\\3\\end{bmatrix}$$

y = \

$$\begin{bmatrix}-5\\-4\\1\\11\\end{bmatrix}$$

1. a table of values is shown:

- 8	- 4	0	4	8

which equation models the relationship in the table?
c. y = \frac{3}{4}x - 6

1. the graph of a line is shown on the coordinate grid below.

which linear equation represents the graph?
a. y - 2 = - \frac{2}{3}x
b. y - 2 = - \frac{3}{2}(x + 1)
c. y + 1 = - \frac{2}{3}(x - 2)
d. y + 1 = - \frac{3}{2}(x - 2)

1. a research firm determined that the s(t)=2t + 80 can be used to model the spending by tourists in florida, s, in billions of dollars, for the years 2013 - 2017 where t is the number of years since 2013. what is the meaning of s(0)?

a. the amount of money spent by tourists in 1973.
b. the amount of money spent by tourists in 2093.
c. the amount of money spent by tourists in 2013.

Explanation:

1. Rewrite \(8x - 12y=48\) in slope - intercept form (\(y = mx + b\))

Step1: Isolate the \(y\) - term

Subtract \(8x\) from both sides of the equation \(8x - 12y=48\):
\(-12y=-8x + 48\)

Step2: Solve for \(y\)

Divide each term by \(-12\):
\(y=\frac{-8x}{-12}+\frac{48}{-12}\)
Simplify to get \(y = \frac{2}{3}x-4\)

Step1: Expand the right - hand side

Use the distributive property \(a(b - c)=ab - ac\), so \(y - 3=4x-8\)

Step2: Rearrange the terms

Subtract \(4x\) from both sides and add 3 to both sides: \(-4x + y=- 5\) or \(4x-y = 5\)

Step1: Find the slope \(m\)

The line passes through two points, say \((-1,2)\) and \((1,-1)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-1 - 2}{1+1}=-\frac{3}{2}\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((-1,2)\), the equation is \(y - 2=-\frac{3}{2}(x + 1)\)

Answer:

D. \(y=\frac{2}{3}x - 4\)

2. Rewrite \(y - 3=4(x - 2)\) in standard form (\(Ax+By = C\))