Question
Line L passes through the point (4, 10).
(a) Find the gradient of line L.
(b) Write down the equation of line L, in the form y = mx + c.
(c) Line P passes through the point (0, 0).
Line P is parallel to line L.
Write down the equation of line P.
▶️Answer/Explanation
(a) To find the gradient of line L, we can use the formula:
Gradient (m) = (change in y) / (change in x)
We have the coordinates (4, 10) and (0, -2) on line L. The change in y is -2 – 10 = -12, and the change in x is 0 – 4 = -4. Therefore, the gradient of line L is:
\(m=\frac{-12}{-4}=3\)
(b) To write down the equation of line L in the form y = mx + c, we need to determine the y-intercept, c.
We know that line L passes through the point (4, 10). Substituting these values into the equation, we get:
10 = 3\times 4 + c
10 = 12 + c
c = 10 – 12 = -2
Therefore, the equation of line L is:zy = 3x – 2
(c) Line P is parallel to line L and passes through the point (0, 0). Since line P is parallel to line L, it will have the same gradient, which is 3. Therefore, the equation of line P is:
y = 3x
Question
(a)
The line AB is drawn on the grid.
(i) Write down the co-ordinates of A.
(ii) Work out the gradient of the line AB.
(iii) Write down the equation of the line AB in the form y = mx + c.
y = ……………….
(b) Write down the equation of a straight line that is parallel to y = 5x – 3.
Answer/Explanation
Ans:
(a) (i) 0, 1
(ii) 2
(iii) [y =] 2x + 1 final answer
(b) y = 5x + c oe final answer
Question
y = mx + c
Find the value of y when m = −2, x = −7 and c = −3.
y = …………………..
Answer/Explanation
Ans:
11
Question
Write down the equation of line l.
Give your answer in the form y = mx + c.
y = …………………………………………..
Answer/Explanation
Ans:
y = 3x – 1