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.
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.
Sure! I can help you step-by-step with the y and x-intercept, as well as the points on a graph.
2.1.1 To find the gradient, we need to look at the coefficient of x in the equation. In this case, the equation is y = 2x - 5, so the gradient is 2.
2.1.2 To find the y-intercept, we need to look at the constant term in the equation. In this case, the equation is y = 2x - 5, so the y-intercept is -5.
2.2.1 To determine the value of the unknown point k in the equation y = -1/3x - 2, we can substitute the given y-coordinate (-1) into the equation and solve for x. So, we have:
-1 = (-1/3)k - 2
Adding 2 to both sides, we get:
1 = (-1/3)k
Multiplying both sides by -3, we get:
-3 = k
Therefore, the value of k is -3.
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 point-slope form of the equation y - y1 = m(x - x1).
Let's find the equation using point A(-2/3, 1):
Using the point-slope form, we have:
y - 1 = m(x - (-2/3))
Now, we need to find the slope (m):
m = (y2 - y1) / (x2 - x1)
Using points B(-2, 1/2) and A(-2/3, 1), we have:
m = (1/2 - 1) / (-2 - (-2/3))
m = (1/2 - 1) / (-2 + 2/3)
m = (1/2 - 1) / (-6/3 + 2/3)
m = (1/2 - 2/2) / (-4/3)
m = (-1/2) / (-4/3)
m = (-1/2) * (-3/4)
m = 3/8
Substituting the slope and the coordinates of point A into the equation, we have:
y - 1 = (3/8)(x - (-2/3))
y - 1 = (3/8)(x + 2/3)
y - 1 = (3/8)x + (3/8)(2/3)
y - 1 = (3/8)x + 1/4
y = (3/8)x + 1/4 + 1
y = (3/8)x + 5/4
Therefore, the equation of the line is y = (3/8)x + 5/4 in the form of y = mx + c.
I hope this helps! Let me know if you have any further questions.
Sure, I can help you with that! Let's break down each question step by step.
2.1.1 To identify the gradient, we can look at the coefficient of x in the equation. In the given equation, y = 2x - 5, the coefficient of x is 2. Therefore, the gradient is 2.
2.1.2 To find the y-intercept, we need to observe the constant term in the equation. In the given equation, y = 2x - 5, the constant term is -5. Therefore, the y-intercept is -5.
2.2.1 In this question, we are given the equation y = -(1/3)x - 2 and asked to find the value of k for the point (k, -1). To find this, we substitute -1 for y in the equation and solve for x:
-1 = -(1/3)k - 2
To isolate the term with k, we can add 2 to both sides of the equation:
1 = -(1/3)k
To get rid of the coefficient in front of k, we can multiply both sides by the reciprocal of -(1/3), which is -3/1 or -3:
-3(1) = k
-3 = k
Therefore, the value of k for the point (k, -1) is -3.
2.3 To determine the equation of a line given three points, we can use the slope-intercept form of a linear equation, y = mx + c. The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Let's calculate the slope using points A(-2/3, 1) and B(-2, 1/2):
m = (1/2 - 1) / (-2 - (-2/3))
= (-1/2) / (-6/3 + 2/3)
= (-1/2) / (-4/3)
= (3/2) * (-3/4)
= -9/8
Now, let's use one of the points (A or B) to find the y-intercept (c). We'll use point B (-2, 1/2):
1/2 = (-9/8)(-2) + c
1/2 = 9/4 + c
1/2 - 9/4 = c
(2/4) - (9/4) = c
-7/4 = c
Therefore, the equation of the line is y = -9/8x - 7/4.
I hope this explanation helps you understand how to find the gradient, y-intercept, unknown points, and equations of lines in different scenarios.