Question

y=−2x−1

Answer 1

[AI-generated answer — Bot GPT 3.5]

The given equation is in slope-intercept form: y = mx + b.

Comparing with the given equation, we can see that m = -2 and b = -1.

Therefore, the slope of the equation is -2, and the y-intercept is (0, -1).

Answer 2

6x+2y=60

Answer 3

[AI-generated answer — Bot GPT 3.5]

To rewrite the equation in slope-intercept form y = mx + b, let's rearrange the given equation.

6x + 2y = 60

First, subtract 6x from both sides to isolate the term with the variable y.

2y = -6x + 60

Next, divide both sides by 2 to solve for y.

y = (-6x + 60)/2

Simplifying further,

y = -3x + 30

Comparing this equation to the slope-intercept form y = mx + b, we can determine that the slope (m) for the given equation is -3, and the y-intercept (b) is (0, 30).

Answer 4

Solve the system of equations.

3x+4y=48
6x+2y=60

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations:

3x + 4y = 48 --------(1)
6x + 2y = 60 --------(2)

Let's multiply equation (1) by 2, and equation (2) by 4 to eliminate the variable y:

2*(3x + 4y) = 2*48
4*(6x + 2y) = 4*60

This simplifies to:

6x + 8y = 96 --------(3)
24x + 8y = 240 --------(4)

Now, subtract equation (3) from equation (4):

(24x + 8y) - (6x + 8y) = 240 - 96

This simplifies to:

24x - 6x = 144

Combining like terms:

18x = 144

Divide both sides by 18:

x = 8

Now, substitute the value of x into either equation (1) or (2) to solve for y. Let's use equation (2):

6x + 2y = 60

6(8) + 2y = 60

48 + 2y = 60

Subtract 48 from both sides:

2y = 12

Divide both sides by 2:

y = 6

Therefore, the solution to the system of equations is x = 8 and y = 6.

Answer 6

[AI-generated answer — Step-by-Step Bot]

To graph the equation y = -2x - 1, we can start by plotting a few points and then connecting them to form a straight line.

Let's choose some values for x and calculate the corresponding y-values:

When x = 0:
y = -2(0) - 1
y = -1
So we have the point (0, -1).

When x = 1:
y = -2(1) - 1
y = -3
So we have the point (1, -3).

When x = -1:
y = -2(-1) - 1
y = 1
So we have the point (-1, 1).

Now, plot these three points on a coordinate plane. Connect them with a straight line.

The resulting graph should be a straight line that passes through the points (0, -1), (1, -3), and (-1, 1).

Answer 7

[AI-generated answer — Explain Bot]

The equation y = -2x - 1 is in the form of a linear equation in slope-intercept form, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept, which is the point where the line intersects the y-axis.

In the given equation, y = -2x - 1, the coefficient of x is -2, which represents the slope of the line. Since the slope is negative, the line will have a downward slope. The constant term, -1, represents the y-intercept, which is where the line crosses the y-axis. In this case, the line crosses the y-axis at the point (0, -1).

To graph this equation, start by plotting the y-intercept at (0, -1). From there, use the slope to find additional points on the line. The slope of -2 means that for every 1 unit increase in x, the y-value decreases by 2 units. This means you can find another point on the line by moving 1 unit to the right and 2 units down from the y-intercept. Repeat this process to find more points, and then connect them to draw the line.

Alternatively, you can create a table of x and y values to plot the points. Choose a few different x-values, substitute them into the equation to get the corresponding y-values, and then plot the points on a graph.

For example, if you choose x = -1, substitute it into the equation:
y = -2(-1) - 1
y = 2 - 1
y = 1

So, one point you can plot is (-1, 1). Repeat this process to find more points and then connect them to graph the line.