Question

question 4 (1 point)
what is the slope-intercept form of $10x - y - 8 = 0$?
a. $y = -2x$
b. $y = -10x - 8$
c. $y = -10x + 8$
d. $y = 10x - 8$
e. $y = 10x + 8$

a e
b a
c c
d d
e b

question 5 (1 point)
a line in the standard $(x,y)$ coordinate plane has a slope of $\frac{2}{3}$ and passes through points $(3,4)$ and $(t, -2)$. what is the value of $t$?
f. 3
g. 2
h. 0
j. $-2$
k. $-6$

a g
b j
c f
d h
e k

Explanation:

Question 4

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We need to rewrite the equation \(10x - y-8 = 0\) in this form.

Step2: Solve for \(y\)

Start with the equation \(10x - y - 8=0\).
Add \(y\) to both sides of the equation: \(10x-8=y\).
Rearrange the terms to get \(y = 10x-8\).

Step1: Recall the slope formula

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
We know that \(m = \frac{2}{3}\), \(x_1 = 3\), \(y_1=4\), \(x_2=t\) and \(y_2=-2\).

Step2: Substitute the values into the slope formula

Substitute the values into the formula: \(\frac{2}{3}=\frac{-2 - 4}{t - 3}\)
Simplify the numerator of the right - hand side: \(\frac{2}{3}=\frac{-6}{t - 3}\)
Cross - multiply: \(2(t - 3)=-6\times3\)
Expand the left - hand side: \(2t-6=-18\)
Add 6 to both sides: \(2t=-18 + 6=-12\)
Divide both sides by 2: \(t=\frac{-12}{2}=-6\)

Answer:

d. D

Question 5