What are the first two steps to graph [tex]y=\frac{4}{5} x+2[/tex]?
What is the first step?
A. Plot the point [tex](0,2)[/tex].
B. Plot the point [tex](2,0)[/tex].
C. Plot the point [tex](5,4)[/tex].
D. Plot the point [tex](4,5)[/tex].
What is the next step?
A. From this point, move 4 units up (the rise) and 5 units to the right (the run).
B. From this point, move 5 units down (the rise) and 4 units to the left (the run).
C. From this point, move 5 units up (the rise) and 4 units to the right (the run).
D. From this point, move 2 units up (the rise) and [tex]\frac{4}{5}[/tex] units to the right (the run).
Answer (2)
Identify the y-intercept from the equation y = 5 4 x + 2 , which is 2, and plot the point ( 0 , 2 ) .
Use the slope 5 4 to find another point on the line.
From the point ( 0 , 2 ) , move 5 units to the right and 4 units up to find another point.
The first two steps are plotting ( 0 , 2 ) and then moving 4 units up and 5 units to the right. So the answers are A and A. A , A
Explanation
Identify the y-intercept The given equation is in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept. In our equation, y = 5 4 x + 2 , we can identify the y-intercept as 2. This means the line crosses the y-axis at the point (0, 2).
Plot the y-intercept The first step to graphing the line is to plot the y-intercept, which is the point (0, 2). Looking at the options for the first step, option A is 'Plot the point (0, 2)', which matches our analysis.
Use the slope to find another point The slope of the line is 5 4 . The slope represents the 'rise over run', meaning for every 5 units we move to the right on the x-axis (the 'run'), we move 4 units up on the y-axis (the 'rise'). Starting from the y-intercept (0, 2), we move 5 units to the right and 4 units up to find another point on the line.
Determine the next step Therefore, the next step is to move 4 units up (the rise) and 5 units to the right (the run) from the point (0, 2). Looking at the options for the next step, option A is 'From this point, move 4 units up (the rise) and 5 units to the right (the run)', which matches our analysis.
Examples
Understanding how to graph linear equations is essential in many real-world scenarios. For example, if you are tracking the distance you travel over time at a constant speed, you can represent this relationship with a linear equation. The y-intercept would represent your starting point, and the slope would represent your speed. By graphing this equation, you can easily visualize how far you'll travel after a certain amount of time, or how long it will take to reach a specific destination. This is also applicable in business, where linear equations can model costs, revenue, and profit, helping to make informed decisions.
The first step to graph the equation y = 5 4 x + 2 is to plot the point ( 0 , 2 ) , which corresponds to option A. The next step is to move 4 units up and 5 units to the right from this point, also option A. Therefore, both answers are A and A.
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