Can someone explain to me how to find the equation pf the line in the form Ax + By + C =0 if
a) parallel to x=3 and passes through (-4, 3)
b)perpendicular to y=4 and passes through (1, 1)
c) passes through the x-int of y=2x-6 and y-int of y=-3x+6
If it is parallel to x=3, the slope is undefined (vertical line), so it is an x=constant, in this case, x=-4
A=1, B=0, C=4
If it is perpendicular to y=4, then it is a vertical line. X=1
A=1 B=0, C=-1
2*3
To find the equation of a line in the form Ax + By + C = 0, you need to determine the values of A, B, and C.
a) To find the equation of a line parallel to x = 3 and passing through (-4, 3):
Since the line x = 3 is a vertical line parallel to the y-axis, the slope is undefined. For a vertical line, the equation is in the form x = constant, where the constant represents the x-coordinate of any point on the line.
In this case, the line is parallel to x = 3 and passes through (-4, 3). So, we can determine that the equation is x = -4.
Therefore, A = 1, B = 0, and C = -4.
b) To find the equation of a line perpendicular to y = 4 and passing through (1, 1):
The given line y = 4 is a horizontal line parallel to the x-axis. For a horizontal line, the slope is 0. The perpendicular line will have an undefined slope (since the slope is the negative reciprocal of the given slope) and be in the form of y = constant.
In this case, the line is perpendicular to y = 4 and passes through (1, 1). The equation of the perpendicular line is y = 1.
Therefore, A = 0, B = 1, and C = -1.
c) To find the equation of a line passing through the x-intercept of y = 2x - 6 and the y-intercept of y = -3x + 6:
The x-intercept of a line is the point where the line intersects the x-axis, which occurs when y = 0. Similarly, the y-intercept is the point where the line intersects the y-axis, which occurs when x = 0.
For the given lines, y = 2x - 6 and y = -3x + 6, we can set y to 0 and solve for x to find the x-intercept, and set x to 0 and solve for y to find the y-intercept.
For y = 2x - 6:
0 = 2x - 6
2x = 6
x = 3
The x-intercept is (3, 0).
For y = -3x + 6:
y = -3(0) + 6
y = 6
The y-intercept is (0, 6).
Now, we have two points: the x-intercept (3, 0) and the y-intercept (0, 6).
Using these two points, we can calculate the slope of the line:
slope = (change in y) / (change in x)
slope = (0 - 6) / (3 - 0)
slope = -6 / 3
slope = -2
Now, we have the slope (-2) and a point on the line (3, 0). We can use the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope, to find the equation of the line.
Using the point (3, 0) and the slope -2, we have:
y - 0 = -2(x - 3)
y = -2x + 6
Rearranging the equation to bring it in the Ax + By + C = 0 form:
2x + y - 6 = 0
Therefore, A = 2, B = 1, and C = -6.