A line is shown on the coordinate plane.
On coordinate plane, points (2, 1), (1, 5) and (0, 9) are connected through a line.
Drag a number to each box to represent the equation of the line.
The equation of a line can be represented in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula: m = (y2 - y1)/(x2 - x1)
Using the given points (2, 1) and (1, 5), we have:
m = (5 - 1)/(1 - 2) = 4/-1 = -4
Now, we can substitute one of the given points into the equation y = mx + b to solve for b. Let's use the point (2, 1):
1 = -4(2) + b
1 = -8 + b
b = 9
Therefore, the equation of the line is y = -4x + 9
To find the equation of the line passing through the points (2, 1), (1, 5), and (0, 9), let's use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
1. Let's find the slope (m) first. We can use any two points on the line to calculate the slope. Let's use the points (2, 1) and (1, 5).
The slope formula is given by m = (y2 - y1) / (x2 - x1).
Substituting the coordinates of the two points, we get:
m = (5 - 1) / (1 - 2) = 4 / (-1) = -4.
2. Now that we have the slope (m), let's choose one of the given points. Let's use the point (2, 1).
Substituting the values into the point-slope form equation, we get:
y - 1 = -4(x - 2).
3. Simplifying the equation, we have:
y - 1 = -4x + 8.
4. We can rearrange the equation to get the slope-intercept form, y = mx + b:
y = -4x + 9.
So, the equation of the line passing through the points (2, 1), (1, 5), and (0, 9) is y = -4x + 9.
To find the equation of a line, we can use the slope-intercept form:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To calculate the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1)
We can choose any two points on the line to calculate the slope.
Let's use the points (2, 1) and (1, 5):
m = (5 - 1) / (1 - 2)
m = 4 / -1
m = -4
Now we have the slope (m), and we need to find the y-intercept (b). We can use any point on the line to do this. Let's use the point (2, 1):
1 = -4(2) + b
1 = -8 + b
b = 9
Therefore, the equation of the line is:
y = -4x + 9
In the given options, you can drag the number -4 to the first box and the number 9 to the second box to represent the equation of the line.