What is the slope intercept and y-intercept in this equation, y=2/3x + 6 ?

Question

I need to find the slope and y-intercept in the following equation. Can you please help me?

Thank you,

y=2/3x + 6?

Answer 1

This is a straightforward question, because the equation is already in the slope-intercept form, which is

y = mx + b, where m is the slope and b is the y-intercept.

Answer: Slope is 2/3, y-intercept is 6. (<- That's good enough for solving the problem.)

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As a tutor, I always try to squeeze more out of a particular problem. In this case, I might find it useful to mention to a student some or all of the following:

1. The terminology comes from the graph/visual representation of an equation.
2. This is a linear function/equation.
3. The graph of such a function on the coordinate plane is a (straight) line.
4. The "slope of equation", which is in question is the slope of the line, 2/3.
5. The "y-intercept of equation", which is in question, is the y-coordinate of the point where the line intersects the y-axis.
6. Any point on the y-axis has x-coordinate of 0.
7. The y-intercept point has coordinates (0, y-intercept).
8. To graph this equation draw the line through two points (0, y-intercept) and (-9, 0).
9. The second point coming from plugging y = 0 into the equation. 0 = 2/3x + 6. => x = -9.
10. x = -9, is the x-intercept of this equation.

Answer 2

Hi!

Since the equation of the given line is already in slope-intercept form:

y=mx+b

where m is the slope (rise over run that gives the slant of the line)

and b is the y-intercept (the point where it crosses the y-axis)

For y= 2/3 x +6

Slope= 2/3

Y-intercept= (0, 6)

Hopefully, that helps!

:-)

Answer 3

Great question. This equation of a line is in slope-intercept form:

y = mx + b

x = independent variable or input

y = dependent variable or output, also could be written as f(x)

m = slope = rise / run = (change in y) / (change in x) = AKA the constant rate of change of the line

b = y-intercept, the point (0, b) on the y-axis where x = 0 and y = b

In this case, slope m = 2/3 and y-intercept b = 6.

Follow-up question:

To build off this question, how could we graph this line in the coordinate plane?

Depending on the information that we have, we could go about approaching this question in different ways.

[1] If we only have this equation, then I would first graph the y-intercept (0, 6), where x = 0 & y = 6.

[2] Then to graph the next point, I would use the slope. The change in y is 2. The change in x is 3.

Therefore, the second point we could graph would be (0+3, 6+2) --> (3, 8). We only need two points to graph a line.

[3] We plot these two points and the line that passes through both (0, 6) and (3, 8) is our line.

Thank you for the question!

Answer 4

The given equation is already in slope-intercept form: y = mx + b. In that equation m is the slope and b is the y-intercept. The slope here is 2/3 and the y-intercept is 6. If you were looking for the y-intercept as a coordinate pair, it would be (0,6)

Answer 5

The slope-intercept form is y = mx + b and the equation given to us is y = 2/3x + 6 which is already in slope-intercept form. In this form:

1. m represents the slope
2. b represents the y-intercept

If we compare:

y = mx + b

y = 2/3x + 6

We notice, the slope (m) is the number in front of x which would be 2/3 in the equation given to us and y-intercept (b) is 6.

Answer 6

What is the slope intercept and y-intercept in this equation, y=2/3x + 6 ?

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

In the equation, y = 2/3 x + 6, the slope is m = 2/3 and the y-intercept of 6.

Answer 7

What is the slope and y intercept in the following equation y=2/3x + 6

Information required to solve the equation: y=2/3x + 6

The slope intercept form of a linear equation is y=mx + b

1. m is the slope and b is the y intercept

y = 2/3 x + b y = mx + b

Step 1 Identify the slope:

1. The slope (m) is the coefficient of (x) m = 2/3

Step 2 Identify the y intercept

1. y = 2/3 x + b y = mx + b

1. The y intercept (b) is the constant term. b = 6

Solution to the equation y = 2/3 x + 6

The slope is 2/3 and the y intercept is 6

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.

Answer 8

Hi, to answer this question, let us break it down into pieces. We are trying to find the slope and the y-intercept of the equation y=(2/3) x + 6.

The first step is to rearrange the equation into slope-intercept form. We are in luck, and because the equation is already in slope-interest form.

Slope-intercept form is represented in generic terms as y=mx+b, where m is your slope and b is your y-intercept.

To define the slope of a line, and the we are looking at the steepness of the line. It's like how much the line goes up or down as you move front left to right on an xy graph. If it goes up, it is a positive slope. On the other hand, if it goes down it is a negative slope. The steeper the line the bigger the slope.

Also when we refer to an equation of a line in slope-intercept form, which is we are always referring to the y-intercept. The y-intercept is the value of y where the line crosses when x=0.

In our case, the it is already in the correct forn so we just have to plug in the right values.

The slope "m" = - 2/3

The y-intercept "b" = 6

Answer 9

Hey my friend! I want you to use this secret recipe to reach the solution in the easiest possible manner!

The standard form for a straight line equation is y = mx + b

1. m is the slope
2. b is the y-intercept

Applying this for the equation you have, y = 2/3x + 6

1. m = slope = 2/3
2. b = y-intercept = (0,6)

Remember, I offer my online sessions at a very competitive rate of $25/hr and I am always happy to adjust to your availability!!

Answer 10

This equation is written in slope intercept form, y=mx+b, where m is the slope and b is the y value of the y intercept (where x=0). In your equation, y=(2/3)x+6, m=2/3 and b=6. Therefore, the slope is 2/3 and the y-intercept is (0,6).

Answer 11

This equation is already in slope-intercept form, y = mx + b where m is the slope and b is the y-intercept. Therefore we can easily determine that the slope is 2/3 and the y-intercept is 6.

Answer 12

Hello!

Let's approach this question by first trying to identify which form the given equation is in. The current equation, y= 2/3x + 6 mimics the slope-intercept form of linear equations.

Slope intercept form is given by y=mx + b, where y is the output value, m is the slope, x is the independent variable or input value, and b is the y-intercept. Now that we have this information, all we have to do is map our given equation to the slope-intercept form.

Since m = 2/3, our slope is 2/3. This means for every two values of y we go up, we move three units to the right (the x-axis). Similarly, b = 6, which means the y-intercept is 6.

I hope this helps!

Answer 13

Hi,

I'll be happy to help you.

The equation provided is written in Slope-Intercept Form which is y=mx + b

where m is the slope of the line and b is the y-intercept.

Therefore in the equation y=2/3x + 6, m=2/3 which is also the coefficient of x and b=6

Please let me know if you have any other questions.

Thank you,

Nisdaly Finalet

Math Tutor

Licensed Teacher

Master's in Education