Question

topic 5 test

1. in the table below, draw an example of the 4 types of slopes (1 pt each)

negative positive undefined zero
for problems 2 - 4, find the slope and y - intercept (put the slope in simplest form). (2 pts each)

1. y = 3x + 5

slope =
y intercept =

1. find the y intercept (1 pt)
2. find the slope of the points (4,8) and (2,10) (put the slope in simplest form) (2 pts)
3. find the slope of the points (5,-3) and (-1,-3) (put the slope in simplest form) (2 pts)

Explanation:

Problem 2:

Step1: Select two points

Let's take two points on the line from the graph, say $(0, 1)$ and $(2, 4)$.

Step2: Calculate slope formula

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 0,y_1 = 1,x_2=2,y_2 = 4$ gives $m=\frac{4 - 1}{2 - 0}=\frac{3}{2}$.

Step3: Find y - intercept

The y - intercept is the y - value when $x = 0$. From the point $(0,1)$, the y - intercept $b = 1$.

Problem 3:

Step1: Select two points

Take two points on the line from the graph, like $(0,6)$ and $(2,2)$.

Step2: Calculate slope

Using $m=\frac{y_2 - y_1}{x_2 - x_1}$, with $x_1 = 0,y_1 = 6,x_2 = 2,y_2=2$, we get $m=\frac{2 - 6}{2 - 0}=\frac{-4}{2}=-2$.

Step3: Find y - intercept

The y - intercept is the y - value at $x = 0$. From the point $(0,6)$, the y - intercept $b = 6$.

Problem 4:

Step1: Identify slope and y - intercept from equation

The equation of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. For $y = 3x+5$, the slope $m = 3$ and the y - intercept $b = 5$.

Problem 5:

Step1: Find y - intercept from table

The y - intercept is the y - value when $x = 0$. From the table, when $x = 0$, $y = 2$, so the y - intercept $b = 2$.

Problem 6:

Step1: Apply slope formula

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ for the points $(4,8)$ and $(2,10)$ with $x_1 = 4,y_1 = 8,x_2 = 2,y_2 = 10$, we have $m=\frac{10 - 8}{2 - 4}=\frac{2}{-2}=-1$.

Problem 7:

Step1: Apply slope formula

For the points $(5,-3)$ and $(-1,-3)$ with $x_1 = 5,y_1=-3,x_2=-1,y_2 = -3$, using $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m=\frac{-3-(-3)}{-1 - 5}=\frac{-3 + 3}{-6}=0$.

Answer:

Problem 2:
Slope = $\frac{3}{2}$
Y intercept = $1$
Problem 3:
Slope = $-2$
Y intercept = $6$
Problem 4:
Slope = $3$
Y intercept = $5$
Problem 5:
Y intercept = $2$
Problem 6:
Slope = $-1$
Problem 7:
Slope = $0$