SOLUTION: A line passes through the point (4,3) and intersects the x-axis at x=10. Where does the line intersect the y-axis? choose the answer and explain the reason to choose your respon

Question 486598: A line passes through the point (4,3) and intersects the x-axis at x=10. Where does the line intersect the y-axis?
choose the answer and explain the reason to choose your response
y=4.5
y=7.7
y=6
y=5
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
If a line passes through the point (4,3) and intersects the at or at the point (10,0), we can find the equation using these two points:

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

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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.

so, the equation in form is:
...the line intersect the at
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