Question

Urgent, please help me asap? Never tried this before but are you able to answer more than a single question at a time on here? I've a week before the next exam in Algebra 1 and I need all the help I can get, questions are below. As usual, please show me exactly how you got the answer with steps so that I can do it too? Thank you so much in advance.

Answer 1

Refer to the step-by-step explanation.

Explanation:

Below are the solutions to your given questions.

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6) To graph the equation 'y = −3', simply draw a horizontal line at y = -3 on the coordinate plane. See the attached image.

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7) To graph the equation 'y + 4 = 0', start by rearranging the equation:

⇒ y + 4 = 0

∴ y = -4

To graph, simply draw a horizontal line at y = -4 on the coordinate plane. See the attached image.

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8) Given the equation, 'y = x + 3'. Simply plug in the given x-coordinates to find the y-coordinate.

When x = 7:

⇒ y = 7 + 3

⇒ y = 10

∴ (7, 10)

When x = -4:

⇒ y = -4 + 3

⇒ y = -1

∴ (-4, -1)

When x = 0:

⇒ y = 0 + 3

⇒ y = 3

∴ (0, 3)

Thus, our points are: (7, 10), (-4, -1), and (0, 3). Plot these points in the coordinate plane. Then, using a straight edge connect the three points. See attached image.

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The formula to find the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:

`\text{Slope } (m)= (y_2-y_1)/(x_2-x_1)`

In our case, let's define:

• (x₁, y₁) → (2, -6)
• (x₂, y₂) → (4, -12)

Plugging in the given points:

`\Longrightarrow m= (-12-(-6))/(4-2)\\\\\\\\\Longrightarrow m= (-12+6)/(2)\\\\\\\\\Longrightarrow \ m= (-6)/(2)\\\\\\\\\therefore \boxed{m=-3}`

So, the slope of the line that passes through the points (2, -6) and (4, -12) is -3.