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].
Answer (2)
Identify the y-intercept from the equation: y = 5 4 x + 2 has a y-intercept of 2, corresponding to the point ( 0 , 2 ) .
Plot the y-intercept ( 0 , 2 ) on the coordinate plane.
Use the slope 5 4 to find another point on the line. Starting from ( 0 , 2 ) , move 5 units to the right and 4 units up to find the point ( 5 , 6 ) .
The first step is to plot the point ( 0 , 2 ) , so the answer is A .
Explanation
Identify the y-intercept and plot it The equation y = 5 4 x + 2 is in slope-intercept form, y = m x + b , where m is the slope and b is the y-intercept. In this case, the y-intercept is 2, meaning the line crosses the y-axis at the point (0, 2). To graph the line, we first plot this point. Then, we use the slope 5 4 to find another point. The slope tells us that for every 5 units we move to the right on the x-axis, we move 4 units up on the y-axis. So, starting from (0, 2), we move 5 units right to x = 5 and 4 units up to y = 6. This gives us the point (5, 6). We can then draw a line through these two points.
Determine the first step The first step to graph the line is to plot the y-intercept, which is the point (0, 2).
Choose the correct option Comparing this with the given options, we see that option A, 'Plot the point (0,2)', is the correct first step.
Examples
Understanding how to graph linear equations is fundamental in many real-world applications. For instance, if you are tracking the distance a car travels over time at a constant speed, you can represent this relationship with a linear equation. The y-intercept would represent the initial distance, and the slope would represent the speed of the car. By plotting the y-intercept and using the slope to find another point, you can easily visualize the car's journey on a graph. This skill is also useful in financial planning, where you might graph how savings grow over time with a constant interest rate.
The first step in graphing the equation y = 5 4 x + 2 is to plot the point ( 0 , 2 ) , which is the y-intercept. Thus, the correct answer is option A. After this, you can use the slope to find additional points for the line.
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