What are the coordinates of the x-intercept in the equation 3x + 7y = 18?
Answers
Step-by-step explanation:
1.1 Solve 3x+7y-18 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x+7y-18 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 18/7 so this line "cuts" the y axis at y= 2.57143
y-intercept = 18/7 = 2.57143
Calculate the X-Intercept :
When y = 0 the value of x is 6/1 Our line therefore "cuts" the x axis at x= 6.00000
x-intercept = 18/3 = 6
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.571 and for x=2.000, the value of y is 1.714. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.714 - 2.571 = -0.857 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -0.857/2.000 = -0.429
Geometric figure: Straight Line
Slope = -0.857/2.000 = -0.429
x-intercept = 18/3 = 6
y-intercept = 18/7 = 2.57143
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