SOLUTION: Task: A. Graph the function f(x) = –3x + 7. Be sure to properly label the graph, which includes labeling the axes and the line with its equation. B. Graph the fu

Algebra ->  Graphs -> SOLUTION: Task: A. Graph the function f(x) = –3x + 7. Be sure to properly label the graph, which includes labeling the axes and the line with its equation. B. Graph the fu      Log On


   

Question 103166: Task:

A. Graph the function f(x) = –3x + 7. Be sure to properly label the graph, which includes labeling the axes and the line with its equation.

B. Graph the function f(x) = –3x2 + x – 5. Be sure to properly label the graph, which includes labeling the axes and the graph with its equation.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1. Graph the function f%28x%29 = -3x+%2B+7
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=-3%2Ax%2B7 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=0

y=-3%2A%280%29%2B7

y=0%2B7 Multiply

y=7 Add

So here's one point (0,7)




Now lets find another point

Plug in x=1

y=-3%2A%281%29%2B7

y=-3%2B7 Multiply

y=4 Add

So here's another point (1,4). Add this to our graph





Now draw a line through these points

So this is the graph of y=-3%2Ax%2B7 through the points (0,7) and (1,4)


So from the graph we can see that the slope is -3%2F1 (which tells us that in order to go from point to point we have to start at one point and go down -3 units and to the right 1 units to get to the next point), the y-intercept is (0,7)and the x-intercept is (2.33333333333333,0) ,or (7%2F3,0)


We could graph this equation another way. Since b=7 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,7).


So we have one point (0,7)





Now since the slope is -3%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,7), we can go down 3 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=-3%2Ax%2B7


So this is the graph of y=-3%2Ax%2B7 through the points (0,7) and (1,4)


2. Graph the function f%28x%29 = –%283%2A2%29 + x –+5
f%28x%29 = -6%2Ax + x – 5
f%28x%29 = -5x – 5
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=-5%2Ax-5 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-2

y=-5%2A%28-2%29-5

y=10-5 Multiply

y=5 Add

So here's one point (-2,5)




Now lets find another point

Plug in x=-1

y=-5%2A%28-1%29-5

y=5-5 Multiply

y=0 Add

So here's another point (-1,0). Add this to our graph





Now draw a line through these points

So this is the graph of y=-5%2Ax-5 through the points (-2,5) and (-1,0)


So from the graph we can see that the slope is -5%2F1 (which tells us that in order to go from point to point we have to start at one point and go down -5 units and to the right 1 units to get to the next point), the y-intercept is (0,-5)and the x-intercept is (-1,0)


We could graph this equation another way. Since b=-5 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-5).


So we have one point (0,-5)





Now since the slope is -5%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-5), we can go down 5 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=-5%2Ax-5


So this is the graph of y=-5%2Ax-5 through the points (0,-5) and (1,-10)