1.Write an equation in slope- intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(2,-2);y=-x-2
A.y=-2x
B.y=2x ********
C.y=1/2x
D.y=-x
2.Write an equation in slope- intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(2,-1);y=-3/2x-6
A.y=-3/2x+1
B.y=-3/2x-1
C.y=-3/2x+2 *********
D.y=-3/2x+4
3.Write an equation in slope- intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(4,2);x=-3
A.y=2
B.y=2x+4
C.y=4x**************
D.y=4
Is anyone available to check these for me?
#1
Since your new line is to be parallel to y = -x - 2
then it must clearly start as y = -x ...... as well
let new one be y = -x + b, but (2,-2) is on it, so
-2 = -2) + b
b = 0
new one is y = -x
#2, correct
#3, the given line x = -3 is a vertical line
so the vertical line passing through (4,2) must be
x = 4, which is none of the given choices
TYPO!
To find the equation of a line that is parallel to a given line and passes through a given point, you need to consider that parallel lines have the same slope.
1. Given point: (2, -2)
Given equation: y = -x - 2
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Since the line we are looking for is parallel to the given line, it will have the same slope.
The given equation is already in slope-intercept form, with a slope of -1. Therefore, the equation of the line parallel to it that passes through the point (2, -2) will have the same slope and can be written as:
y = -x + b, where b is the y-intercept to be determined.
Substitute the coordinates of the given point (2, -2) into the equation and solve for b:
-2 = -(2) + b
-2 = -2 + b
-2 + 2 = b
0 = b
Therefore, the equation of the line parallel to the given equation and passing through the point (2, -2) is y = -x + 0, or simply y = -x (Option A).
2. Given point: (2, -1)
Given equation: y = -3/2x - 6
Similar to the previous problem, the slope of the line we are looking for will be the same as the slope of the given line, which is -3/2.
Using the slope-intercept form, the equation of the line parallel to it passing through (2, -1) can be written as:
y = -3/2x + b
Substitute the coordinates (2, -1) into the equation to solve for b:
-1 = -3/2(2) + b
-1 = -3 + b
-1 + 3 = b
2 = b
Therefore, the equation of the line parallel to the given equation and passing through the point (2, -1) is y = -3/2x + 2 (Option C).
3. Given point: (4, 2)
Given equation: x = -3
In this case, the given equation is not in slope-intercept form. We know that parallel lines have the same slope, so we need to determine the slope from the given equation.
To convert the equation x = -3 into slope-intercept form, we need to solve it for y. Since x is constant, the line is vertical and intersects the y-axis at y = -3.
Since parallel lines have the same slope, any line parallel to x = -3 will also be vertical with a slope of infinity or undefined.
Therefore, the equation of the line parallel to x = -3 and passing through the point (4, 2) can be written as x = 4 (Option C).