Which is the graph of the line that passes through a point (3,-4) and has a slope of 1/3?
To graph the line, we can use the formula y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope is 1/3.
y = (1/3)x + b
To find b, we need one more point on the line. Luckily, we have a point (3, -4) that the line passes through.
-4 = (1/3)(3) + b
-4 = 1 + b
b = -5
Now we have the equation of the line: y = (1/3)x - 5.
To graph the line, we can plot the y-intercept at (0, -5), and then use the slope to plot one more point.
Rise = 1, Run = 3, starting at (0, -5):
Up 1, right 3 to (3, -4).
We can now draw a straight line through the two points to represent the equation of the line.
The graph of the line that passes through the point (3,-4) and has a slope of 1/3 is:
graph{(1/3)x-5 [-10, 10, -10, 10]}
Graph
I'm sorry, can you please provide more information about what you would like me to graph?
Graph (3,-4)
and has a slope of 1/3
If you only need to graph the point (3,-4) and not the entire line, you can simply plot the point on the Cartesian plane.
The point (3,-4) has an x-coordinate of 3 and a y-coordinate of -4. So, starting at the origin (0,0), we move right 3 units along the x-axis and then down 4 units along the y-axis to plot the point.
The graph of the point (3,-4) is:
graph{(3,-4) [-10, 10, -10, 10]}
To find the graph of a line that passes through a point and has a given slope, we can use the point-slope form of a linear equation.
The point-slope form is given as: y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope.
In this case, the given point is (3, -4) and the slope is 1/3.
Using the point-slope form, we can substitute the values:
y - (-4) = 1/3(x - 3)
Simplifying the equation:
y + 4 = 1/3(x - 3)
Next, we can distribute 1/3 to (x - 3):
y + 4 = 1/3x - 1
Now, let's isolate y by subtracting 4 from both sides of the equation:
y + 4 - 4 = 1/3x - 1 - 4
The equation becomes:
y = 1/3x - 5
Now that we have the equation in y = mx + b form, where m represents the slope and b is the y-intercept, we can interpret it.
The slope of the line is 1/3, which means that for every 1 unit increase in x, y increases by 1/3 unit. This implies that the line will rise at a slower rate as it moves to the right.
The y-intercept (b) is -5, which is the point where the line crosses the y-axis. So, the line passes through the point (0, -5).
To graph the line, plot the point (0, -5) on the graph and use the slope to find other points. For example, using the slope of 1/3 from the y-intercept (0, -5), you can move 1 unit to the right and 1/3 units up to find another point on the line. Repeat this process to get additional points and then connect them to draw the line.
So, the graph of the line that passes through the point (3, -4) and has a slope of 1/3 is a line that rises slowly as it moves to the right and crosses the y-axis at the point (0, -5).