The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below:Step 1: 3(2x − 4) = 8 + 2x + 6
Step 2: 5x − 7 = 14 + 2x
Step 3: 5x − 2x = 14 + 7
Step 4: 3x = 21
Step 5: x = 7

In which step did the student first make an error and what is the correct step?

Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7

Answer:

The answer is y = x + 8

                       y = -x + 7

Answer:

Perpendicular

Step-by-step explanation:

Here, we want to know the relationship between the two lines .

The easiest way to go about this is to get their slopes;

Mathematically, the equation of a straight line can be expressed in the form;

y = mx + c

where m is the slope;

Hence;

2x -5y = 10

Isolating the y part

5y = 2x -10

divide through by 5

y = 2/5x - 2

So the slope here is 2/5

for the second line

10x + 4y = 20

Divide by 2 all through

5x + 2y = 10

Isolate y

2y = 10-5x

Divide by 2 again

y = 5 -5/2x

The slope here is -5/2

What do we notice? we can see that if we multiply the two slopes by each other, we get -1

That is;

2/5 * -5/2 = -1

What this means is that both lines are perpendicular.

This is because the slopes of perpendicular lines, when multiplied by each other = -1

Final answer:

The two given lines, 2x - 5y = 10 and 10x + 4y = 20, intersect at an angle other than 90 degrees. We determined this by finding the slope of each line and seeing that they are neither equal (for parallel lines) nor negative reciprocals (for perpendicular lines).

Explanation:

To determine the relationship between the lines 2x - 5y = 10 and 10x + 4y = 20, we need to analyze their slopes. Both equations can be rewritten in slope-intercept form (y = mx + b) to determine their slopes. The first equation becomes y = (2/5)x - 2, and the second equation becomes y = (-10/4)x + 5.

The slopes of the two lines are m1 = 2/5 and m2 = -10/4. Since the slopes are different, the lines are not parallel. To determine if they are perpendicular, we need to check if their slopes are negative reciprocals.

The product of the slopes is (2/5)(-10/4) = -4/5. Since the product is not -1, the lines are not perpendicular. Therefore, the correct relationship is that the lines intersect at an angle other than 90 degrees.

Learn more about Relationship between two lines here:

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Answer:

2

Step-by-step explanation:

You called this question to the right person. To find the y-intercept, you must do the formula of Point Slope (y-y1 = m (x-x1)) Since 2, is x1 and the -1 is y1, we must lay the equation out like this: y - -1 = m (x-2). Next, we must distribute the slope to the x and the 2, which would allow the x, to fit in with the slope, and the 2 to become 1 since 1/2 x 2 is 1. Now what we need to do is get rid of the -1, so what we do here is add 1. And algebra golden rule, whatever you do to one side, you must do to the other side. This would leave y = 1/2x + 2 And therefore 2 is your y-intercept, since it's at the last part of the equation.