Graph the line with the given point and slope.
Through (1,1); slope= -4/5
To graph the line with the given point (1,1) and slope -4/5, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Plugging in the values, we have:
y - 1 = (-4/5)(x - 1)
Now, let's rearrange the equation into slope-intercept form (y = mx + b), where b is the y-intercept:
y - 1 = (-4/5)x + 4/5
Simplifying further:
y = (-4/5)x + 4/5 + 1
y = (-4/5)x + 4/5 + 5/5
y = (-4/5)x + 9/5
Now we have the equation of the line in slope-intercept form. To graph it, plot the given point (1,1) and use the slope to find additional points. The slope is -4/5, which means for every 5 units you move to the right, you will move 4 units downward.
Using this information, we can plot the point (1,1) and find additional points by moving 5 units to the right and 4 units down from the previous point.
Using (1,1) as the starting point:
(1, 1)
(6, -3)
(11, -7)
(16, -11)
Connect the points, and you will have the graph of the line.
To graph a line with a given point and slope, you can follow these steps:
1. Plot the given point (1, 1) on the coordinate plane. This will serve as one point on the line.
2. Use the slope (-4/5) to find the next point. The slope represents the change in the y-coordinate (vertical change) over the change in the x-coordinate (horizontal change). Start from the given point (1, 1) and move down 4 units and to the right 5 units. This will give you the second point on the line.
3. Connect the two points with a straight line. This line represents the equation of the given line.
To summarize, the graph of the line passing through the point (1, 1) with a slope of -4/5 would look like this:
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(1,1)
Note that the line may extend beyond the given points in both directions.
To graph the line with a given point and slope, you'll need to use the point-slope form of the equation of a line.
The point-slope form of a line is: y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the given point and m represents the slope.
In this case, the given point is (1, 1) and the slope is -4/5. So our equation becomes:
y - 1 = (-4/5)(x - 1)
Now, we can rearrange the equation to get it in slope-intercept form (y = mx + b), which will allow us to easily plot the line. Start by distributing the -4/5:
y - 1 = (-4/5)x + 4/5
Next, move -1 to the other side of the equation:
y = (-4/5)x + 4/5 + 1
y = (-4/5)x + 4/5 + 5/5
y = (-4/5)x + 9/5
Now that the equation is in slope-intercept form, we can see that the slope is -4/5 and the y-intercept (b) is 9/5.
To graph the line, plot the given point (1, 1) and use the slope to find additional points.
Starting from the given point (1, 1), you'll move down 4 units (the numerator of the slope) and to the right 5 units (the denominator of the slope). This gives us the point (6, -3). Repeat this process to find more points if needed.
Once you have a few points, connect them with a straight line. This line represents the graph of the equation y = (-4/5)x + 9/5.