The graph is attached.
f(x) = x + 1 where x < 0
f(x) = 2 where 0 ≤ x ≤ 1
f(x) = x where x > 1
The graph in the attached figure
x-------> the input (independent variable)
y-------> the output (dependent variable)
we know that
The equation that represent the situation is equal to
This is a linear equation
To graph the line find the intercepts
The y-intercept is equal to the point ---> value of y when the value of x is equal to zero
The x-intercept is equal to the point ---> value of x when the value of y is equal to zero
Plot the points
the graph in the attached figure
substitue values in the table into the equation.
x = 2, then y = 4(2)-3 =>
y = -3, then -3 = 4x-3 =>
x = 0
x = -1, then y = 4(-1) - 3 =>
y = -7
x = 3, then y = 4(3) -3 =>
y = 9
y = 1, then 1 = 4x - 3 =>
x = 4
now plot all of these points and create a line from them
Plot the y-intercept, (0, 4).
Placing your pencil point there first, move it 5 units to the right and 4 up, arriving at (5, 4+4), or (5, 8).
From (5, 8), move your pencil point 5 units to the right and 2 units down, ending up at (10, 8-2), or (10, 6).
Connect (0, 4) and (5, 8) with a line segment.
Also connect (5, 8) and (10, 6) with a line segment.
Step by step hope this helps
My blue dot is the y-intercept.
My red dot is my x-intercept.
Please look at the graph.
I can show you my graph and mark it where the x-intercepts and y-intercepts are.
We have y=2/3 x+4.
Compare this to the slope-intercept form, y=mx+b where m is the slope and b is the y-intercept.
You should see that m=2/3 and b=4.
This means the slope is 2/3 and the y-intercept is 4.
Don't forget slope means rise/run.
So once we graph 4 (plot a point) on the y-axis, then we will use our slope to get to one more point. The slope here tells us to rise 2 and run 3.
Now sometimes our graph is not accurate when drawing by hand so there is a way without graphing that you can find the x- and y-intercepts.
The x-intercept is when the y-coordinate is 0.
The y-intercept is when the x-coordinate is 0.
So to find the x-intercept, I'm going to set y to 0 and solve for x. Like so,
0=2/3 x +4
Subtract 4 on both sides:
Multiply both sides by the reciprocal of 2/3 which is 3/2:
So the x-intercept is (-6,0).
I actually already have the y-intercept since my equation is in y=mx+b (slope-intercept form). But if it wasn't you could just set x to 0 and solve for y. Like so:
The y-intercept is (0,4).
Let's go to our graph now.
I think x = 1 but I’m not sure I’m sorry
f(X) = 10 + 5X
f(X) is the total hours for that week
X is the week number after this plan was put in place
10 is the y-intercept; this is when X=0 which is when
the plan went into effect
5 is the change in the y-value for a change of 1 in the
X-value; this will raise the number of games he can
play by 5 each additional week
After 6 weeks Peter would have 36 total hours of gaming. All you have to do is plug 6 in for x, so you would multiply 6 * 4 = 24 and add 12 which equals 36. The number 12 in the equation equals the number of hours Peter played last week, 4 equals the number of hours Peter's parents let him pay per week, and x equals the number of weeks Peter plays his favorite game. Hope this helps.
then look at the points giving to u and plot them on the graph