The slope of a line is given by the ratio of the rise to the run of the line.
The value of, y is <u>4</u>
Reasons:
The given points on the line are; (-4, y), and (5, 7)
The slope of the line, =
Required:
To find the value of <em>y</em>
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Solution:
The formula for the slope is given as follows;
Where;
(x₁, y₁) = (-4, y)
(x₂, y₂) = (5, 7)
Which gives;
3·(7 - y) = 1·(5 + 4) = 9
21 - 3·y = 9
3·y = 21 - 9 = 12
The value of, y = <u>4</u>
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(3, -2) and (2, 1) are solutions to the inequality y <= 3/2x - 1
<h3>How to determine the inequality?</h3>The complete question is added as an attachment
The points are given as:
(3, -2) and (2, 1)
Next, we test the points on each inequality in the list of options.
So, we have:
<u>Option 1</u>
y > 1/2x + 2
Substitute (3, -2) and (2, 1) for x and y
-2 > 1/2 * 3 + 2 ⇒ -2 > 3.5 -- false
2 > 1/2 * 1 + 2 ⇒ 2 > 2.5 -- false
Hence, (3, -2) and (2, 1) are not solutions to the inequality y > 1/2x + 2
<u>Option 2</u>
y <= 3/2x - 1
Substitute (3, -2) and (2, 1) for x and y
-2 <= 3/2 * 3 - 1 ⇒ -2 <= 3.5 -- true
1 <= 3/2 * 2 - 1 ⇒ 1 < 2 -- true
Hence, (3, -2) and (2, 1) are solutions to the inequality y <= 3/2x - 1
<u>Option 3</u>
y >= 4x - 2
Substitute (3, -2) and (2, 1) for x and y
-2 >= 4 * 3 - 2 ⇒ -2 >= 10 -- false
2 <= 4 * 2 - 2 ⇒ 2 <= 6 -- false
Hence, (3, -2) and (2, 1) are not solutions to the inequality y >= 4x - 2
<u>Option 4</u>
y < -2x + 1
Substitute (3, -2) and (2, 1) for x and y
-2 < -2 * 3 + 1 ⇒ -2 < -5 -- false
2 < -2 * 2 + 1 ⇒ 2 < -3 -- false
Hence, (3, -2) and (2, 1) are not solutions to the inequality y < -2x + 1
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