Confused mom thanks for your help.
Find the X and Y intercepts of the line that passes through the given points (-6,4), (3,-5)
slope = m = [ -5 - 4 ] / [ 3 - -6]
= -9/9
= -1
so
y = -x + b
4 = 6 + b
so
b = -2
so equation is
y = -x -2
x axis intercept when y = 0
so (-2,0)
y axis intercept when x = 0
so (0, -2)
In this case :
x1 = - 6 , y1 = 4
x2 = 3 , y2 = - 5
Equation of a straight line from 2 points :
y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] ( x - x1 )
y = 4 + [ ( - 5 - 4 ) / ( 3 - ( - 6 ) ) ] ( x - ( - 6 ) )
y = 4 + [ ( - 9 ) / ( 3 + 6 ] ( x + 6)
y = 4 + [ ( - 9 ) / 9 ] ( x + 6)
y = 4 + ( - 1 ) ( x + 6)
y = 4 + [ - 1 * x + ( - 1 ) * 6 ]
y = 4 - x - 6
y = - x - 2
x - intercept is a point on the graph where y = 0
y - intercept is a point on the graph where x = 0
So :
x - intercept
y = - x - 2 = 0
- x - 2 = 0 Add 2 to both sides
- x - 2 + 2 = 0 + 2
- x = 2 Multiply both sides by - 1
x = - 2
Coordinates of x - intercept :
x = - 2 , y = 0
OR
( - 2 , 0 )
y - intercept
y = - x - 2
x = 0
y = - ( 0 ) - 2 = 0 - 2 = - 2
Coordinates of y - intercept :
x = 0 , y = - 2
OR
( 0 , - 2 )
To find the x and y-intercepts of a line, we need to determine the points where the line crosses the x-axis (x-intercept) and the y-axis (y-intercept).
Step 1: Find the equation of the line using the given points.
To find the equation of a line, we can use the point-slope formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
Using the given points (-6,4) and (3,-5):
Let's calculate the slope first.
slope (m) = (change in y) / (change in x)
= (-5 - 4) / (3 - (-6))
= -9 / 9
= -1
Now, let's pick one of the points (let's use (-6,4)) and substitute the values into the point-slope formula to find the equation of the line:
y - 4 = -1(x - (-6))
y - 4 = -1(x + 6)
y - 4 = -x - 6
y = -x - 2
So, the equation of the line passing through the points (-6,4) and (3,-5) is y = -x - 2.
Step 2: Find the x-intercept.
To find the x-intercept, we need to determine the point where the line crosses the x-axis. This occurs when y = 0.
Substitute y = 0 into the equation y = -x - 2, and solve for x:
0 = -x - 2
x = -2
Therefore, the x-intercept is (-2,0).
Step 3: Find the y-intercept.
To find the y-intercept, we need to determine the point where the line crosses the y-axis. This occurs when x = 0.
Substitute x = 0 into the equation y = -x - 2, and solve for y:
y = -0 - 2
y = -2
Therefore, the y-intercept is (0,-2).
In summary, the x-intercept is (-2,0) and the y-intercept is (0,-2).