The graph of 4x + 2y= 5 cuts the x axis at point A and the y axis at point B. Find the:
Coordinates of point A.
Gradient of line A B.
At the x-axis, the y value is zero, so let y = 0
4x + 0 = 5
x = 5/4 , so point A is (5/4 , 0)
At the y-axis, the x value is zero, so let x = 0
0 + 2y = 5
y = 5/2 , so point B is (0 , 5/2)
slope = (5/2-0)/(0 - 5/4) = 2
other way:
if you have a linear equation of the form x/a + y/b = 1
then a is the x-intercept, and b is the y-intercept and the slope is b/a
4x+ 2y = 5
divide each term by 5
4x/5 + 2y/5 = 1
x/(5/4) + y/(5/2) = 1 , see the intercepts ?
slope = (5/2) / (5/4) = (5/2)(4/5) = 2
Draw the graph of the line represent by the equation
To find the coordinates of point A, we need to find the x-intercept of the graph, where the line crosses the x-axis.
To find the x-intercept, we set y = 0 and solve for x in the equation 4x + 2y = 5.
Plugging in y = 0, we have:
4x + 2(0) = 5
4x = 5
x = 5/4
Therefore, the coordinates of point A are (5/4, 0).
To find the gradient (slope) of line AB, we need to find the slope of the line passing through points A and B.
The formula for calculating the slope between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Since point B lies on the y-axis, its x-coordinate is 0, and its y-coordinate is the y-intercept of the line.
Plugging in the coordinates of A (x1 = 5/4, y1 = 0) and B (x2 = 0, y2 = y-intercept), we have:
m = (y-intercept - 0) / (0 - 5/4)
m = y-intercept / (-5/4)
To find the y-intercept, we set x = 0 in the equation 4x + 2y = 5 and solve for y.
Plugging in x = 0, we have:
4(0) + 2y = 5
2y = 5
y = 5/2
So, the y-intercept is 5/2.
Plugging this value back into the equation for the slope, we have:
m = (5/2) / (-5/4)
m = -2/4 = -1/2
Therefore, the gradient (slope) of line AB is -1/2.
To find the coordinates of point A, we need to determine the x-intercept of the graph.
The x-intercept occurs when the y-coordinate is equal to zero. So, let's substitute y = 0 into the equation of the line and solve for x:
4x + 2(0) = 5
4x = 5
x = 5/4
Therefore, the x-coordinate of point A is 5/4.
Now, let's find the gradient of line AB. The gradient represents the ratio of the change in y-coordinates to the change in x-coordinates between two points.
Since point A is on the x-axis and point B is on the y-axis, the change in y-coordinates is equal to the y-coordinate of point B, and the change in x-coordinates is equal to the x-coordinate of point A.
Therefore, the gradient of line AB is given by:
Gradient = (y-coordinate of B) / (x-coordinate of A)
Gradient = (0) / (5/4)
Gradient = 0
Hence, the gradient of line AB is 0.