Complete the following statements using m(x) = x² and n(x) = x – 3.
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Answer:
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: where m is the slope and b is the y-intercept (the value of y when x is 0).
<u>1) Determine the slope (m)</u>
where two points on the line are
and
In the graph, the points (-3,-6) and (2,-2) are plotted clearly, so we can use these to help us find the slope. Plug them into the equation:
Therefore, the slope of the line is . Plug this into
:
<u>2) Determine the y-intercept (b)</u>
Typically, given a graph, we could look at where exactly the line crosses the y-axis to determine b. However, because it appears ambiguous on this graph, we must solve it algebraically.
Plug in one of the given points (2,-2) and solve for b:
Subtract from both sides to isolate b
Therefore, the y-intercept of the line is . Plug this back into
:
I hope this helps!