SOLUTION: The x- and y-intercepts of the graph of g are 1 and 4, respectively. What is the linear equation satisfying the given condition.

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Question 459109: The x- and y-intercepts of the graph of g are 1 and 4, respectively. What is the linear equation satisfying the given condition.
Found 2 solutions by oberobic, MathLover1:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
y = mx + b
.
When x=0, y = 4 (given)
(0,4)
.
When y=0, x = 1 (given)
(1,0)
.
Recall that the change in y divided by the change in x = slope.
.
Change in y = 4-0 = 4
Change in x = 0-1 = -1
Slope = 4/-1 = -4
.
The equation is thus:
y = -4x +4
.
The graph is:
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-4%2Ax%2B4%29
.
Notice that the y-intercept is (0,4), the x-intercept is (1,0), and the line goes through both points.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The x-intercept is (1,0) and
y-intercept is (0, 4)
these are two points on a line and now let's find equation:

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,0) and (0,4)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (1,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,4))


m=%284-0%29%2F%280-1%29 Plug in y%5B2%5D=4,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=1 (these are the coordinates of given points)


m=+4%2F-1 Subtract the terms in the numerator 4-0 to get 4. Subtract the terms in the denominator 0-1 to get -1




m=-4 Reduce



So the slope is

m=-4





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-0=%28-4%29%28x-1%29 Plug in m=-4, x%5B1%5D=1, and y%5B1%5D=0 (these values are given)



y-0=-4x%2B%28-4%29%28-1%29 Distribute -4


y-0=-4x%2B4 Multiply -4 and -1 to get 4%2F1. Now reduce 4%2F1 to get 4

y=-4x%2B4%2B0 Add 0 to both sides to isolate y


y=-4x%2B4 Combine like terms 4 and 0 to get 4

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Answer:



So the equation of the line which goes through the points (1,0) and (0,4) is:y=-4x%2B4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-4 and the y-intercept is b=4


Notice if we graph the equation y=-4x%2B4 and plot the points (1,0) and (0,4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-4x%2B4 through the points (1,0) and (0,4)


Notice how the two points lie on the line. This graphically verifies our answer.