Question 403757: Using the graph, determine the value of y when x=4.
The graph shows a forward slanting line the crosses -3 on the y-axis and 1.5 on x axis..
how do i figure this out?
Found 2 solutions by nerdybill, MathLover1:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Find 4 on the x-axis.
Then, go straight up until you hit the slant line.
then, go horizontally (to the left) until you hit the y-axis.
Where you connect with the y-axis is your answer (should be 5)
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website!
given:
Using the graph, determine the value of  when  .
line the crosses  on the  ...means you have one point at (0,-3)
and  on  axis....means you have second point at (1.5, 0)
now, we can find EQUATION of straight line given  points
| Solved by pluggable solver: FIND EQUATION of straight line given 2 points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (0, -3) and (x2, y2) = (1.5, 0).
Slope a is  .
Intercept is found from equation  , or  . From that,
intercept b is  , or  .
y=(2)x + (-3)
Your graph:
|
from the graph you can see, if you draw a line parallel to from the point  it will cross your line at 
that is the value of when ; your third point is (4,5)
let's check if all three your points are collinear (lie on same line)
| Solved by pluggable solver: To determine if 3 points lie in a line |
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.
Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.
Slope of line taking points (X1,Y1) and (X2,Y2) is
 ........................(1)
Slope of line taking points (X3,Y3) and (X1,Y1) is
 ........................(2)
From conditions (1) and (2)
The slopes are equal hence the 3 points can lie on same line.
If the slope calculated from points (X2,Y2) and (X3,Y3) comes out to be same then it is confirmed that the 3 points lie on a same line.
 ........................(3)
From (1),(2) and (3)
Hence, It is proved that the 3 points lie on same line.
To read more on equations of a line refer to articles on wikipedia
|
|
|
|
