| {{ 'ml-lesson-number-slides' | message : article.intro.bblockCount }} |
| {{ 'ml-lesson-number-exercises' | message : article.intro.exerciseCount }} |
| {{ 'ml-lesson-time-estimation' | message }} |
Here is a recommended reading before getting started with this lesson.
The intercepts of a line provide information about the position of the line in the coordinate plane. They can be used to identify the equation of a line from known points or to graph a line from its equation.
The applet shows the graphs of different lines. Identify the intercepts of these lines.
A linear equation is an equation with at least one linear term and any number of constants. No other types of terms may be included. Linear equations in one variable have the following form, where a and b are real numbers and a=0.
Linear equations in two variables have the form below, where a, b, and c are real numbers and a=0 and b=0.
A linear equation can be written in the following form called the slope-intercept form.
y=mx+b
In this form, m is the slope and b is the y-intercept. These are the general characteristics or parameters of the line. They determine the steepness and the position of the line on the coordinate plane. Consider the following graph.
This line has a slope of 2 and a y-intercept of 1. The equation of the line can be written in slope-intercept form using these values.
The following applet generates linear equations. Those equations represent the relation between two variables x and y. Determine whether the generated equation is in slope-intercept form.
Finally, use a straightedge to draw a line through both points.
This line is the graph of y=2x−3.
Jordan is investigating the fish population in Grassy Lake. The number of fish in the lake was counted as 60 in 2016.
She finds out that the population increases by 120 after each year. The following equation represents the fish population in the lake.y-intercept: Number of fish in the year 2016
Next, move 1 unit to the right and 120 units up from the y-intercept to plot another point.
Finally, the graph of the equation can be competed by drawing a line passing through these two points.
Note that the number of years passed or the number of fish cannot be negative. Therefore, only the first quadrant of the coordinate plane is shown.
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This line intercepts the y-axis at (0,-4), which means that the y-intercept is -4.
Jordan turns her attention to the cheetah population over years.
She finds a graph on the Internet that shows the number of cheetahs over years since 1900.
Jordan wants to represent the graph algebraically to interpret it further.
y-intercept: Number of cheetahs in the year 1900
rise=-40000, run=50
Put minus sign in front of fraction
Calculate quotient
y=0
LHS+800x=RHS+800x
LHS/800=RHS/800
Calculate quotient
Substitute (-4,1) & (8,4)
a−(-b)=a+b
Add and subtract terms
Calculate quotient
x=8, y=4
Multiply
LHS−2=RHS−2
Rearrange equation
Jordan is interested in endangered animals. She reads a magazine to learn what can be done to save these animals.
Suppose Jordan reads the same number of pages each day. The following table shows the number of pages y left in the magazine after x days.
Number of Days x | 5 | 9 | 15 |
---|---|---|---|
Number of Pages y | 147 | 95 | 17 |
Write an equation for the given situation in slope-intercept form using the Slope Formula.
Number of Days x | 5 | 9 | 15 |
---|---|---|---|
Number of Pages y | 147 | 95 | 17 |
Point (x,y) | (5,147) | (9,95) | (15,17) |