Question

geometry prep: quiz 3 - 7 & 3 - 8
slope of a line $m = \frac{y_2 - y_1}{x_2 - x_1}$
slope - intercept form of a linear equation $y=mx + b$
point - slope form of a linear equation $y - y_1=m(x - x_1)$

1. what is the ordered pair for point a?

a) (3, 2) b) (2, 3) c) (-3, 2) d) (-3, -2)

1. find the slope of a line with the points (-6, 3) and (-2, 10).
2. tell whether the lines through the given points are parallel, perpendicular, or neither.

line 1: (-6, 0)(8, 7)
line 2: (1, 4)(2, 2)
a) parallel b) perpendicular c) neither

1. write an equation in slope intercept form of the line that passes through (-5, -4) and is parallel to $y = 4x-2$.

a) $y = 4x + 16$ b) $y=-\frac{1}{4}x - 3$ c) $y = 4x + 5$ d) $y=-4x - 24$
slope of a line $m = \frac{y_2 - y_1}{x_2 - x_1}$
slope - intercept form of a linear equation $y=mx + b$
point - slope form of a linear equation $y - y_1=m(x - x_1)$

Explanation:

Step1: Determine point A's coordinates

Point A is 3 units to the left of the y - axis (x = - 3) and 2 units above the x - axis (y = 2), so the ordered pair is (-3, 2).

Step2: Calculate the slope for question 2

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)=(-6,3)$ and $(x_2,y_2)=(-2,10)$. Then $m=\frac{10 - 3}{-2-(-6)}=\frac{7}{4}$.

Step3: Calculate slopes for question 3

For Line 1 with $(x_1,y_1)=(-6,0)$ and $(x_2,y_2)=(8,7)$, $m_1=\frac{7 - 0}{8-(-6)}=\frac{7}{14}=\frac{1}{2}$. For Line 2 with $(x_1,y_1)=(1,4)$ and $(x_2,y_2)=(2,2)$, $m_2=\frac{2 - 4}{2 - 1}=-2$. Since $m_1\times m_2=\frac{1}{2}\times(-2)=-1$, the lines are perpendicular.

Step4: Find the equation for question 4

Parallel lines have the same slope. The slope of $y = 4x-2$ is $m = 4$. Use the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(-5,-4)$. So $y+4 = 4(x + 5)$, expand to get $y+4=4x + 20$, then $y=4x+16$.

Answer:

1. C. (-3, 2)
2. $\frac{7}{4}$
3. B. Perpendicular
4. A. $y = 4x + 16$