Write down the gradient and the y-intercept of the straight lines whose equations are given as follows: a) y=2x-4, b) 2y=x+6, c) y-x=2, d) 2x+3y=6-x
Put each equation into the form
y = mx + b. You will have to frearrange some of them.
The "gradient" (or slope) is then m and the y-intercept is b.
For example, in (a), m = 2 and b = -4.
To find the gradient and y-intercept of a straight line given its equation, we can compare the equation with the standard form of a straight line, which is y = mx + b.
a) Equation: y = 2x - 4
Comparing this equation with the standard form, we find that the gradient (m) is 2, and the y-intercept (b) is -4. Therefore, the gradient is 2, and the y-intercept is -4.
b) Equation: 2y = x + 6
To find the equation in the standard form, we need to isolate y. Dividing both sides by 2, we get y = (1/2)x + 3. Comparing this with the standard form, we find that the gradient (m) is 1/2, and the y-intercept (b) is 3. Therefore, the gradient is 1/2, and the y-intercept is 3.
c) Equation: y - x = 2
Rearranging the equation to the standard form, we get y = x + 2. Comparing this with the standard form, we find that the gradient (m) is 1, and the y-intercept (b) is 2. Therefore, the gradient is 1, and the y-intercept is 2.
d) Equation: 2x + 3y = 6 - x
Rearranging the equation to the standard form, we get 3y + x = 6 - 2x. This can be further simplified to y = (-1/3)x + 2. Comparing this with the standard form, we find that the gradient (m) is -1/3, and the y-intercept (b) is 2. Therefore, the gradient is -1/3, and the y-intercept is 2.
In summary:
a) Gradient = 2, Y-intercept = -4
b) Gradient = 1/2, Y-intercept = 3
c) Gradient = 1, Y-intercept = 2
d) Gradient = -1/3, Y-intercept = 2