2.1.1 The gradient is the coefficient of the x-term in the equation, which is 2.
2.1.2 The y-intercept is the constant term in the equation, which is -5.
Therefore, the values representing the gradient and the y-intercept from the equation y=2x-5 are:
2.1.1 Gradient = 2
2.1.2 Y-intercept = -5
2.2 To determine the value of the unknown point k, we can substitute the given point (-1, -1) into the equation y = -1/3x - 2.
Substituting -1 for y and -1 for x, we have:
-1 = (-1/3)(-1) - 2
Simplifying the equation:
-1 = 1/3 - 2
-1 = 1/3 - 6/3
-1 = -5/3
To find the value of k, we can isolate it by multiplying both sides of the equation by -3:
-3 * (-1) = -3 * (-5/3)
3 = 5k
Dividing both sides by 5:
3/5 = k
Therefore, the value of k is 3/5.
2.2.1 The point (k, -1) corresponds to (3/5, -1).
2.3 To determine the equation of the line using the given points A(-2/3, 1), B(-2, 1/2), and C(0, 3), we can use the slope-intercept form of a linear equation: y = mx + c, where m is the gradient and c is the y-intercept.
Using points A(-2/3, 1) and C(0, 3), we can calculate the gradient (m):
m = (y2-y1)/(x2-x1)
m = (3-1)/ (0 - (-2/3))
m = 2/(2/3)
m = 2 * 3/2
m = 6/2
m = 3
Now, we can choose one of the given points to substitute into the equation and solve for the y-intercept (c). Let's use point A:
1 = 3*(-2/3) + c
1 = -2 + c
c = 1 + 2
c = 3
Therefore, the equation of the line in the form of y = mx + c, using the given points, is:
y = 3x + 3.
can you please help with the y and the x- intercept , i don't understand it
Question 2- Graphs
2.1 identify the values representing the gradient and the y-intercept from the equation.
y=2x-5
2.1.1 gradient
2.1.2 y-intercept
2.2 determine the value of the unknown point k, if the points i on the graph:
y=-1/3x -2
2.2.1 (k, -1)
2.3 three points A(-2/3, 1) ;B (-2; 1/2) and C(0;3), are points on a straight-in graph.
use the points to determine the equation of the line in the form of y = mx +c.
1 answer