Question

question 20
which point lies on the line with point-slope equation $y - 2 = 5(x - 6)$?
a. $(6, -2)$
b. $(6, 2)$
c. $(-6, 2)$
d. $(-6, -2)$

question 21
what is the point-slope equation of a line with slope -4 that contains the point $(-2, 7)$?
a. $y - 7 = -4(x + 2)$
b. $y + 7 = -4(x - 2)$
c. $y - 7 = -4(x - 2)$
d. $y + 7 = -4(x + 2)$

question 22
which expression gives the area of the triangle shown below?
a. $\frac{1}{2}rx$
b. $(\frac{1}{2}p)(\frac{1}{2}x)$
c. $(\frac{1}{2}r)(\frac{1}{2}x)$
d. $\frac{1}{2}px$

question 23
what is the area of a triangle with a base of 9 units and a height of 7 units?
a. 126 sq. units
b. 31.5 sq. units
c. 63 sq. units
d. 15.75 sq. units

Explanation:

Question 20

Step1: Recall point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)$ is a point on the line.

Step2: Match given equation to form

For $y - 2 = 5(x - 6)$, $x_1=6$, $y_1=2$, so the point is $(6,2)$.

Question 21

Step1: Recall point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $m$ is slope, $(x_1,y_1)$ is the point.

Step2: Substitute values

Here $m=-4$, $x_1=-2$, $y_1=7$. Substitute: $y - 7 = -4(x - (-2))$, which simplifies to $y - 7 = -4(x + 2)$.

Question 22

Step1: Recall triangle area formula

Area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.

Step2: Identify base and height

Base is $r$, height is $x$. Substitute into formula: $\frac{1}{2}rx$.

Question 23

Step1: Recall triangle area formula

Area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.

Step2: Substitute values

Base $=9$, height $=7$. Calculate: $\frac{1}{2} \times 9 \times 7 = 31.5$.

Answer:

Question 20: B. (6, 2)
Question 21: A. $y - 7 = -4(x + 2)$
Question 22: A. $\frac{1}{2}rx$
Question 23: B. 31.5 sq. units