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.

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) (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:

.
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) (Show Source): You can put this solution on YOUR website!

The is (1,0) and
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 (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

------------------------------------------------

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

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

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

Plug in , , and (these values are given)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

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

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