Question

1. what is the slope - intercept form of $6x - 2y - 4 = 0$?

a. $y = 6x - 2$
b. $y = 3x + 2$
c. $y = 3x - 2$
d. $y = - 3x + 2$
e. $y = - 6x - 4$

1. which of the following is a solution to the equation $x^{2}+25x = 0$?

a. 10
b. 25
c. 5
d. - 5
e. - 25

1. the length $l$, in meters, of a spring is given by the equation $l=left(\frac{2}{3}

ight)f + 0.05$, where $f$ is the applied force in newtons. approximately what force, in newtons, must be applied for the springs length to be 0.23 meters?
a. 0.12
b. 0.18
c. 0.20
d. 0.24
e. 0.27

Explanation:

Step1: Solve the first equation for slope - intercept form

The slope - intercept form is \(y = mx + b\). Given \(6x-2y - 4=0\), first isolate \(y\).

$$
LATEXBLOCK0
$$

Step2: Solve the second equation \(x^{2}+25x = 0\)

Factor out \(x\): \(x(x + 25)=0\). Then \(x=0\) or \(x=-25\)

Step3: Solve the third equation for \(F\)

Given \(L=\frac{2}{3}F+0.05\) and \(L = 0.23\). Substitute \(L\) into the equation:

$$
LATEXBLOCK1
$$

Answer:

1. C. \(y = 3x-2\)
2. E. \(-25\)
3. E. \(0.27\)