Consider the line L with equation y + 2x = 3. The line L1
is parallel to L and passes through the
point (6, –4).
(a) Find the gradient of L1
.
(b) Find the equation of L1
in the form y = mx + b.
(c) Find the x-coordinate of the point where line L1 crosses the x-axis.
Answers
Answer:
(a) The gradient ( which is I assume the slope) is -2.
(b) The equation of L1 is y = -2x + 8.
(c) The co ordinates are (4,0).
Step-by-step explanation:
(a) As we know that L and L1 are parallel to each other, the equation for L is y + 2x = 3. And the slope for this equation is -2 as y = mx + c.
y = -2x + 3.
(b) The equation of L1 can be found using the formula y-y1 = m(x-x1).
(y+4) = -2(x -6)
y +4 = -2x + 12
y = -2x + 8.
(c) Substitute 0 for y as the x axis co ordinate is (x,0).
0 = -2x + 8
2x = 8
x = 4.
Thus the co ordinate is (4,0).
Let me know if this is the correct answer.
SOLUTION
TO DETERMINE
Consider the line L with equation y + 2x = 3. The line L1
is parallel to L and passes through the point (6, –4).
(a) Find the gradient of L1
(b) Find the equation of L1 in the form y = mx + b.
(c) Find the x-coordinate of the point where line L1 crosses the x-axis.
EVALUATION
The given equation of the line L is
y + 2x = 3
Since the line L1 is parallel to L
Let the equation of the line is
y + 2x = c - - - - - - (1)
The line given by Equation 1 passes through the point (6, –4)
So we have
- 4 + ( 2 × 6 ) = c
⇒ - 4 + 12 = c
⇒ c = 8
The equation of the line L1 is
y + 2x = 8
(a) The equation of the line L1 is y + 2x = 8
Which can be rewritten as
y = - 2x + 8
Which is of the form y = mx + b
m = Gradient of the line = - 2
b = y - intercept of the line = 8
The gradient of L1 = - 2
(b) The equation of the line L1 is y + 2x = 8
Which can be rewritten as
y = - 2x + 8
Which is of the form y = mx + b
m = Gradient of the line = - 2
b = y - intercept of the line = 8
(c) The equation of the line L1 is y + 2x = 8
The line crosses the x-axis
So we have y = 0
Putting y = 0 in above equation we get
0 + 2x = 8
⇒ 2x = 8
⇒ x = 4
So the point is (4,0)
Hence the required x-coordinate of the point where line L1 crosses the x-axis = 4
━━━━━━━━━━━━━━━━
Learn more from Brainly :-
Find the point where the graph of 0.25x + 0.05y =1.00 intersects the y-axis:
https://brainly.in/question/26332017
2. Find the equation of straight line passing through the point (-4,5) and making equal intercepts on the coordinate axis.
https://brainly.in/question/25257443
3. Find the slope of the line perpendicular to the line AB, if A is (3, 3) and B is (-1, 1)
https://brainly.in/question/27031626