Write an equation of the line that passes through the points (1, 2) and (4, 8)
2 answers:
Answer:
y = 2x
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, 8)
m = =
= 2 , then
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 2 )
2 = 2 + c ⇒ c = 2 - 2 = 0
y = 2x ← equation of line
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20 = 2x
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(change in y)/(change in x) = (-18 -(-20))/(1 - 0) = 2
so can be written in slope-intercept form as
g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
10 = x
The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.