Question

keisha is reading a novel for her english class. she has already read some of the book. she starts reading again today and uses the equation ( y = 25x + 50 ) to find the total number of pages, ( y ), she has read after ( x ) hours. graph the equation.
i can start by looking at the given ______ equation. i see that it is written as ( y = mx + b ), which is in ______.
i know that ( m ) is the ______ and ( b ) is the ______.
so, the slope of the given equation is ______ and the ( y )-intercept is ______.
to graph the equation, i can use the ( y )-intercept to plot a point on the ________. that point is ( (0, 50) ).
then i can use the slope to plot another point. the slope is the ______ over the ____, or ( \frac{\text{change in } y}{\text{change in } x} ). the slope is 25, or ( \frac{25}{1} ), so for every increase of ______ in ( x ), there is an increase of 25 in ( y ). that helps me plot another point, ( (1, 75) ).
i can draw a ________ through those two points to graph the equation.
word bank
line
linear
point
rise
run
slope
slope - intercept form
x - axis
y - axis
y - intercept
number bank
1
2
25
50
75

Explanation:

1. The equation \( y = 25x + 50 \) is a linear equation. So the first blank (describing the equation type) is "linear".
2. The form \( y=mx + b \) is the slope - intercept form of a linear equation. So the second blank is "slope - intercept form".
3. In the slope - intercept form \( y = mx + b \), \( m \) represents the slope and \( b \) represents the \( y \)-intercept. So the third blank is "slope" and the fourth blank is "y - intercept".
4. For the equation \( y=25x + 50 \), comparing with \( y = mx + b \), \( m = 25 \) and \( b = 50 \). So the fifth blank (slope) is "25" and the sixth blank (\( y \)-intercept) is "50".
5. The \( y \)-intercept is a point on the \( y \)-axis. So the seventh blank is "y - axis".
6. The slope is defined as the rise over the run (where rise is the change in \( y \) and run is the change in \( x \)). So the eighth blank is "rise" and the ninth blank is "run".
7. For the slope \( \frac{25}{1} \), the change in \( x \) (run) is 1. So the tenth blank is "1".
8. To graph a linear equation, we draw a line through the two points. So the eleventh blank is "line".

Answer:

1. linear
2. slope - intercept form
3. slope; y - intercept
4. 25; 50
5. y - axis
6. rise; run
7. 1
8. line