A pair of equations is shown below: y = 6x − 4 y = 5x − 3 Part A: In your own words, explain how you can solve the pair of equat
ions graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points) Part B: What is the solution to the pair of equations? (4 points)
2 answers:
Answer:
see below
Step-by-step explanation:
A Since both equations are in slope intercept form, we can plot the y intercept for each equation and the use the slope to draw lines. The see where the lines intersect.
y = 6x − 4 slope is 6 , y intercept is (0,-4)
y = 5x − 3 slope is 5 y intercept is (0,-3)
They intersect at (1,2)
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<u>Given</u>:
The given graph passes through the points (-3,4) and (3,2)
The x - axis represents the years. The value x = 5, year 2015.
We need to determine the y - value for 2010.
<u>Slope</u>:
The slope of the line can be determined using the formula,
Substituting the points (-3,2) and (3,2), we get;
Thus, the slope of the line is
<u>y - intercept:</u>
The y - intercept in the graph is the point in the line that crosses the y - axis.
Thus, from the graph, it is obvious that the y - intercept is b = 3.
<u>Equation of the line:</u>
The equation of the line can be determined using the formula,
Substituting the values, we have;
Thus, the equation of the line is
<u>The y - value for 2010:</u>
Since, it is given that x = 5 represents 2015 and 2010 is 5 years before 2010.
Hence, the value of x for 2010 is given by
Thus, x = 0 represents the year 2010.
To determine the y - value, let us substitute x = 0 in the equation , we have;
Thus, for 2010 the value of y is 3.