Question

unit 5 test
personal goal: class goal:
find the x- and y-intercept of each question algebraically then graph both problems -
show all work for full credit! (3 points each)

1. submitted by daniel o per. 8

1.
$y = \frac{4}{3}x - 8$

1. submitted by audrina s per.8

$5x - 10y = 25$
find the slope of the line that passes through the given two points (2 pts)

1. $(-4, -3)$ $(4, 0)$

graph the following lines on the coordinate grid - color code the lines to make them clear. (2 pts)

1. $y = 6$

$x = 8$

Explanation:

Problem 1: \( y = \frac{4}{3}x - 8 \)

Step 1: Find Y - intercept

To find the Y - intercept, we set \( x = 0 \) in the equation \( y=\frac{4}{3}x - 8 \).
Substituting \( x = 0 \) into the equation: \( y=\frac{4}{3}(0)-8=0 - 8=-8 \). So the Y - intercept is \( (0,-8) \).

Step 2: Find X - intercept

To find the X - intercept, we set \( y = 0 \) in the equation \( y=\frac{4}{3}x - 8 \).
We have the equation \( 0=\frac{4}{3}x-8 \).
First, add 8 to both sides: \( 8=\frac{4}{3}x \).
Then, multiply both sides by \( \frac{3}{4} \): \( x = 8\times\frac{3}{4}=6 \). So the X - intercept is \( (6,0) \).

Problem 2: \( 5x - 10y = 25 \)

Step 1: Find Y - intercept

Set \( x = 0 \) in the equation \( 5x-10y = 25 \).
Substituting \( x = 0 \): \( 5(0)-10y=25\Rightarrow - 10y=25\Rightarrow y=\frac{25}{-10}=-\frac{5}{2}=-2.5 \). So the Y - intercept is \( (0,-\frac{5}{2}) \).

Step 2: Find X - intercept

Set \( y = 0 \) in the equation \( 5x - 10y=25 \).
Substituting \( y = 0 \): \( 5x-10(0)=25\Rightarrow5x = 25\Rightarrow x = 5 \). So the X - intercept is \( (5,0) \).

Problem 3: Find the slope between \( (-4,-3) \) and \( (4,0) \)

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \( (x_1,y_1)=(-4,-3) \) and \( (x_2,y_2)=(4,0) \).

Step 2: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{0-(-3)}{4-(-4)}=\frac{0 + 3}{4 + 4}=\frac{3}{8} \).

Problem 4: Graph \( y = 6 \) and \( x = 8 \)

• For the line \( y = 6 \): This is a horizontal line. A horizontal line has the equation \( y = k \), where \( k \) is a constant. For all values of \( x \), \( y = 6 \). So we can plot the points \( (x,6) \) for any \( x \) (e.g., \( (0,6),(1,6),(-1,6) \)) and draw a horizontal line through these points.
• For the line \( x = 8 \): This is a vertical line. A vertical line has the equation \( x = k \), where \( k \) is a constant. For all values of \( y \), \( x = 8 \). So we can plot the points \( (8,y) \) for any \( y \) (e.g., \( (8,0),(8,1),(8,-1) \)) and draw a vertical line through these points.

Answer:

s:

1. For \( y=\frac{4}{3}x - 8 \): Y - intercept \( (0,-8) \), X - intercept \( (6,0) \)
2. For \( 5x - 10y = 25 \): Y - intercept \( (0,-\frac{5}{2}) \), X - intercept \( (5,0) \)
3. Slope between \( (-4,-3) \) and \( (4,0) \) is \( \frac{3}{8} \)
4. \( y = 6 \) is a horizontal line, \( x = 8 \) is a vertical line (graph as described above)