Find the point of intersection by graphing both lines and observing where they intersect.

Question

Y = -4x + 2
Y = x - 3

Answer 1

To find the point of intersection, we will graph both lines and observe where they intersect.

First, let's graph the first line, y = -4x + 2.

We can start by finding the y-intercept, which is the value of y when x = 0.

When x = 0, y = -4(0) + 2 = 2.
So the y-intercept is (0, 2).

Next, we can find the x-intercept, which is the value of x when y = 0.

When y = 0, -4x + 2 = 0.
Solving this equation, we get -4x = -2, which means x = 1/2.
So the x-intercept is (1/2, 0).

Now, let's graph the line y = x - 3.

Again, we start by finding the y-intercept, which is the value of y when x = 0.

When x = 0, y = (0) - 3 = -3.
So the y-intercept is (0, -3).

Next, we find the x-intercept, which is the value of x when y = 0.

When y = 0, x - 3 = 0.
Solving this equation, we get x = 3.
So the x-intercept is (3, 0).

Now, we can graph both lines on the same coordinate plane.

The first line, y = -4x + 2, has a y-intercept of (0, 2) and an x-intercept of (1/2, 0).

The second line, y = x - 3, has a y-intercept of (0, -3) and an x-intercept of (3, 0).

Plotting these points and drawing the lines, we get the following graph:

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-4| *
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-8|______________________
-4 -2 0 2 4

From the graph, we can see that the two lines intersect at the point (1, -2).

Answer 2

Find the point of intersection by graphing both lines and observing where they intersect.
Y = ½ x - 4
Y = -½ x - 1

Answer 3

To find the point of intersection, we will graph both lines and observe where they intersect.

First, let's graph the first line, y = 1/2x - 4.

We can start by finding the y-intercept, which is the value of y when x = 0.

When x = 0, y = 1/2(0) - 4 = -4.
So the y-intercept is (0, -4).

Next, we can find the x-intercept, which is the value of x when y = 0.

When y = 0, 1/2x - 4 = 0.
Solving this equation, we get 1/2x = 4, which means x = 8.
So the x-intercept is (8, 0).

Now, let's graph the line y = -1/2x - 1.

Again, we start by finding the y-intercept, which is the value of y when x = 0.

When x = 0, y = -1/2(0) - 1 = -1.
So the y-intercept is (0, -1).

Next, we find the x-intercept, which is the value of x when y = 0.

When y = 0, -1/2x - 1 = 0.
Solving this equation, we get -1/2x = 1, which means x = -2.
So the x-intercept is (-2, 0).

Now, we can graph both lines on the same coordinate plane.

The first line, y = 1/2x - 4, has a y-intercept of (0, -4) and an x-intercept of (8, 0).

The second line, y = -1/2x - 1, has a y-intercept of (0, -1) and an x-intercept of (-2, 0).

Plotting these points and drawing the lines, we get the following graph:

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--------------*---------------
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-6

From the graph, we can see that the two lines intersect at the point (2, -3).

Answer 4

Tell whether the ordered pair is a solution of the equation. Just substitute the given x and y to see if the equation “works”. Write “solution” if it works and “not solution” if it doesn’t.
y=4x + 2; (2,10)
2x + y = 5; (7, 5

Answer 5

To determine if the given ordered pairs are solutions of the equations, we will substitute the given x and y values into the equations and check if they are true statements.

1. y = 4x + 2
Substituting x = 2 and y = 10:
10 = 4(2) + 2
10 = 8 + 2
10 = 10

Since the equation is true when substituting the given x and y values, the ordered pair (2,10) is a solution.

2. 2x + y = 5
Substituting x = 7 and y = 5:
2(7) + 5 = 5
14 + 5 = 5
19 = 5

Since the equation is not true when substituting the given x and y values, the ordered pair (7,5) is not a solution.

Therefore, the ordered pair (2,10) is a solution for the equation y = 4x + 2, while the ordered pair (7,5) is not a solution for the equation 2x + y = 5.

Answer 6

Set up a table of values:
Y(1) = 1/2x + 5
Y(2) = -2x -1

x
y(1)
1/2x+5
y(2)
-2x - 1
(x,y(1))
(x, y(2))
8

4

0

-2

Set up a table of values:
Y(1) = 1/2x + 5
Y(2) = -2x -1

x
y(1)
1/2x+5
y(2)
-2x - 1
(x,y(1))
(x, y(2))
8

4

0

-2

Set up a table of values: Y(1) = 1/2x + 5 Y(2) = -2x -1 x y(1) 1/2x+5 y(2) -2x - 1 (x,y(1)) (x, y(2)) 8 4 0 -2