A line, y = mx + b, passes through the point (1, 6) and is parallel to y =4x - 6
Answers
EXPLANATION.
Line y = mx + c.
Passes through the point = (1,6).
Parallel to the line : y = 4x - 6.
As we know that,
Slope of the line : y = mx + c.
Slope : = m.
Slope = m = 4.
Put the value of line and slope in equation, we get.
⇒ y = 4x - c.
⇒ 6 = 4(1) - c.
⇒ 6 = 4 - c.
⇒ 6 - 4 = -c.
⇒ 2 = -c.
⇒ c = -2.
Equation of line : y = 4x - 2.
x-intercept of line.
Put the value of y = 0 in equation, we get.
⇒ y = 4(0) - 2.
⇒ y = -2.
Y-intercept of line.
Put the value of x = 0 in equation, we get.
⇒ 0 = 4x - 2.
⇒ 4x = 2.
⇒ x = 2/4.
⇒ x = 1/2.
x-intercept = 1/2 & y-intercept = -2.
MORE INFORMATION.
Point of inflection.
If at any point p, the curve is concave on one side and convex on other side with respect to x-axis, then the point p is called the point of inflection. Thus p is a point of inflection if at p,
d²y/dx² = 0 but d³y/dx³ ≠ 0.
Also point p is a point of inflection if,
f''(x) = f'''(x) = ,,,,,,,,,= fⁿ⁻¹(x) = 0 and fⁿ(x) ≠ 0 for odd n.
Step-by-step explanation:
Line y = my + c
passes through the point = (1,6).
parallel to the line :y = 4x-6.
answer know that,
slope of the line : y = my + 6
slope := m
slope = m=4
put the value of line and slope in equation, we
get.
= y = 4(1) -c
= 6=4(1) -c
= 6=4-c
=6-4=-c
=2=-c
= c =-2
Equation of line :y =4x-2.
x - intercept of line.
put the value of y = 0 in equation, we get.
=y = 4 (0) -2
= y = -2
y - intercept of line
put the value of x = 0 in equation, we get
=0=4x-2
=4x -2
=x= 2/4
= x = 1/2
x = intercept = 1/2 and y - intercept = 2 .
hope it's help us.