Given a line containing the points(1,4), (2,7) and (3,10) determine that slope-intercept form of the equation, provide one additional point on this line, and graph the funtion.
Start by putting the first point into point-slope form: y-y1=m(x-x1), so y-4=m(x-1). Slope, or m, is y2-y1 over x2-x1. With the first two points, slope=7-4 over 2-1, or 3 over 1, which is 3. The equation is then y-4=3(x-1). After doing basic algebra, the slope-intercept form of the equation is y=3x+1.
Using the slope of 3, add three to the y-value of the last point, (3,10), and 1 to the x-value; you are basically doing the slope equation backwards here. Your new point could be (4,13).
To graph the function, just plot the points you were given; in fact, you only need 2 of them, and then draw your line.
i would say (4,13) or (0,1) depending which direction you want to go.
the way i see it is like this.
for the point (1,4) to get to the next point (2,7) they are going up 1 number on the x coordinate point and 3 on the y coordinate point.I know that theres a formula for this but i can't remember what it is but i just know that you line is a diagnol line.
I just set up two equations and solved them simultaneously.
y = mx + b
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substitute points 1,4 and 2,7
eqn 1:   4=m(1)+b
eqn 2:   7=m(2)+b
solve for m and b.
m=3 and b=1
from work done by the two previous posters, both 4,13 and 0,1 are on the line as well as the third point given in the problem of 3,10. And y = 3x+1 is the slope intercept form.
I just thought I would give an alternative method of solving the problem.
To find the slope-intercept form of the equation, you can use the formula (y - y1) = m(x - x1) and substitute one of the points given. Let's use the first point (1,4):
(y - 4) = m(x - 1)
To find the slope (m), you can use the formula m = (y2 - y1) / (x2 - x1) with the first two points (1,4) and (2,7):
m = (7 - 4) / (2 - 1)
m = 3 / 1
m = 3
Now we can substitute the slope into the equation:
(y - 4) = 3(x - 1)
Now, let's convert this equation into slope-intercept form (y = mx + b):
y - 4 = 3x - 3
y = 3x + 1
So, the slope-intercept form of the equation is y = 3x + 1.
To find an additional point on this line, we can use the slope. Let's add three to the y-coordinate of the last point (3,10) and one to the x-coordinate:
New point = (3 + 1, 10 + 3)
New point = (4, 13)
So, an additional point on this line is (4,13).
Now, to graph this function, plot the three points: (1,4), (2,7), and (4,13). Then, draw a line passing through these points.
Note: The answer provided by the previous poster, (0,1), is not on the line defined by the given points.
To determine the slope-intercept form of the equation, we can use the given points (1,4), (2,7), and (3,10).
First, find the slope (m) using the formula: m = (y2 - y1)/(x2 - x1)
Using (1,4) and (2,7) as our points: m = (7-4)/(2-1) = 3/1 = 3
Next, choose any of the given points, let's say (1,4), and use the point-slope form: y - y1 = m(x - x1)
Substitute the values: y - 4 = 3(x - 1)
Simplify: y - 4 = 3x - 3
Rearrange to slope-intercept form: y = 3x + 1
Now, to find an additional point on this line, we can use the slope of 3. Let's choose (3,10). By moving 1 unit in the x-direction and 3 units in the y-direction, we get the point (4,13).
To graph the function, plot the points (1,4), (2,7), (3,10), and (4,13) on a coordinate plane. Then, draw a straight line through these points. The line represents the equation y = 3x + 1.