Question 999642: http://172.85.76.57/Library/00001230_84_617_A1.png Can someone help
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52915)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! your picture is shown here.
you look for two points on the graph where the coordinate points are integers.
the two points on that graph are (-1,-2) and (0,1).
you use those two points to find the slope.
slope is equal to (y2-y1)/(x2-x1)
let (0,1) = (x2,y2)
let (-1,-2) = (x1,y1)
(y2-y1) = 1 - (-2) = 3
(x2-x1) = 0 - (-1) = 1
slope is (y2-y1) / (x2-x1) = 3/1 = 3
y-intercept is the value of y when x = 0.
looking at your graph, it appears that the y-intercept is at y = 1.
if it's not clear, you can solve for it as follows:
slope intercept form of the equation is y = mx + b
m is the slope
b is the y-intercept
once you find the slope, then m becomes that slope.
in this case m = 3 and the equation becomes:
y = 3x + b
you can use any one of the points to find the y-intercept.
we'll use (-1,-2)
replace x with -1 and y with -2 and the equation of y = 3x + b becomes:
-2 = -1 * 3 + b
simpkify to get -2 = -3 + b
add 3 to both sides of the equation to get -2 + 3 = b
solve for b to get b = 1.
since the point (0,1) was on the graph and easily identifiable, this was not necessary, but if the line crosses the y-axis at a point that is not an integer, then being able to find it by formula is very helpful.
the other way of finding the y-intercept is by using the point slope form of the equation.
that form is y - y1 = m * (x-x1)
either point can be assigned to (x1,y1).
we'll use (-1,-2) again.
the formula becomes y - (-2) = 3 * (x - (-1)) which then becomes:
y + 2 = 3 * x + 3
subtract 2 from both sides of this equation to get:
y + 2 - 2 = 3 * x + 3 - 2.
simplify to get:
y = 3x + 1
1 is the y-intercept.
i prefer the first method because it's more straight forward and you don't need to remember the point slope form of the eqaution.
all you need to do is remember to replace x and y in the equation with the x-coordinatre and the y-coordinate of any point on the line and solve for b.
your equation becomes y = 3x + 1
the graph of that equation is shown below:
here's a trick for finding the slope.
look for 2 points on the line where the x-coordinate and the y-coordinate are integers.
those points will be at the intersection of the horizontal and vertical grid lines where the horizontal grid is on an integer and the vertical grid is on an integer.
once you find that, use those two points to find the slope.
look at the following line and figure out where the line crosses the intersection of grid lines of integers.
if you picked the points (-7,-5), (0,-2), (7,1), you did good, because that's exactly where they are.
here's the same graph with those points identified.
all that's left is to find the slope and then the y-intercept.
you can use any 2 of those points to find the slope.
we'll use (-7,-5) and (7,1)
the slope is (y2-y1) / (x2-x1)
we'll let (x2,y2) = (7,1) and we'll let (x1,y1) = (-7,-5)
you have:
(x2,y2) = (7,1)
(x1,y1) = (-7,-5)
(y2-y1) = 1 - (-5) = 1 + 5 = 6
(x2-x1) = 7 - (-7) = 7 + 7 = 14
(y2-y1)/(x2-x1) becomes 6/14 which can be simplified to 3/7.
that's your slope.
the y intercept is the value of y when x is equal to 0.
from the graph, you can see that the value of y when x = 0 is at the coordinate point of (0,-2) which means that the y-intercept is y = -2.
the slope intercept formula of the equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept.
your slope is 3/7.
your y-intercept is -2.
your equation is y = 3/7 * x - 2
the same graph with the equation that created it is now shown below:
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