What happens to y as x gets larger?
What happens to x as y gets larger?
d) Given a line containing the points (1,4), (2,7), and (3,10) determine the slope-intercept form of the equation, provide one additional point on this line, and graph the function.
Equation in Slope-Intercept Form:
slope=7-4 over 2-1, or 3 over 1, which is 3. The equation is then y-4=3(x-1).
Show your work here: 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.
Give one additional point in (x,y) form that would fall on this line:
Graph:
if y=3x +1 as x gets larger, y gets larger.
then x=y/3 -1 as y gets larger, x gets larger.
To answer the first question, "What happens to y as x gets larger?" we can examine the equation of the line. In this case, the equation is y = 3x + 1. As x gets larger, the value of 3x also gets larger, so y will also get larger. This means that as x increases, y increases as well.
For the second question, "What happens to x as y gets larger?" we can rearrange the equation to solve for x. The given equation y = 3x + 1 can be rewritten as x = (y - 1) / 3. As y gets larger, the numerator (y - 1) also gets larger, which means that x will also get larger. Therefore, as y increases, x increases as well.
Now, let's move on to the last question, which involves determining the slope-intercept form of the equation, providing an additional point, and graphing the function.
To find the slope-intercept form of the equation given the points (1,4), (2,7), and (3,10), we need to calculate the slope first. The formula for calculating slope is (y2 - y1) / (x2 - x1).
Using the first two points, we have:
slope = (7 - 4) / (2 - 1) = 3 / 1 = 3
Now that we have the slope, we can use the point-slope form of the equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using the point (1,4), we have:
y - 4 = 3(x - 1)
Simplifying the equation gives us:
y - 4 = 3x - 3
To convert it into slope-intercept form (y = mx + b), we isolate y:
y = 3x + 1
So, the equation in slope-intercept form is y = 3x + 1.
To provide an additional point on this line, we can choose any x-value and substitute it into the equation to find the corresponding y-value. Let's say we choose x = 4:
y = 3(4) + 1
y = 12 + 1
y = 13
Therefore, the additional point on this line is (4, 13).
Finally, 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 passing through these points to represent the graph of the function y = 3x + 1.