High School Math : Intercepts and Curves

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Intercepts And Curves

What is the y-intercept of the equation?

\displaystyle y=5x+5

Possible Answers:

\displaystyle (0,1)

\displaystyle (0,25)

\displaystyle (0,\frac{1}{5})

\displaystyle (0,0)

\displaystyle (0,5)

Correct answer:

\displaystyle (0,5)

Explanation:

To find the y-intercept, we set the \displaystyle x value equal to zero and solve for the value of \displaystyle y.

\displaystyle y=5x+5

\displaystyle y=5(0)+5

\displaystyle y=0+5

\displaystyle y=5

Since the y-intercept is a point, we want to write our answer in point notation: \displaystyle (0,5).

Example Question #1 : How To Find X Or Y Intercept

What is the x-intercept of the equation?

\displaystyle y=\frac{2}{3}x+ 12

Possible Answers:

\displaystyle (-12,0)

\displaystyle (6,0)

\displaystyle (-18,0\displaystyle )

\displaystyle (\frac{2}{3},0)

\displaystyle (0,0)

Correct answer:

\displaystyle (-18,0\displaystyle )

Explanation:

To find the x-intercept of an equation, set the \displaystyle y value equal to zero and solve for \displaystyle x.

\displaystyle y=\frac{2}{3}x+ 12

\displaystyle 0 =\frac{2}{3}x+12

Subtract \displaystyle 12 from both sides.

\displaystyle 0 -12 = \frac{2}{3}x +12 - 12

\displaystyle -12 = \frac{2}{3} x

Multiply both sides by \displaystyle \frac{3}{2} .

\displaystyle (\frac{3}{2})(-12) = (\frac{2}{3} x)(\frac{3}{2})

\displaystyle -18= x

Since the x-intercept is a point, we will want to write it in point notation: \displaystyle (-18,0\displaystyle )

Example Question #63 : Coordinate Geometry

What is the y-intercept of \displaystyle y=5x+20?

Possible Answers:

\displaystyle 20

\displaystyle 15

\displaystyle 4

\displaystyle 100

\displaystyle \frac{1}{4}

Correct answer:

\displaystyle 20

Explanation:

To solve for the y-intercept, set the x value equal to zero:

\displaystyle y=5x+20

\displaystyle y=5(0)+20

\displaystyle y=20

Example Question #1 : Intercepts And Curves

What is the x-intercept of \displaystyle y=5x+20?

Possible Answers:

\displaystyle -4

\displaystyle -\frac{1}{4}

\displaystyle 4

\displaystyle 5

\displaystyle 20

Correct answer:

\displaystyle -4

Explanation:

To solve for the x-intercept, set the y value equal to zero:

\displaystyle y=5x+20

\displaystyle 0=5x+20

Subtract \displaystyle 20 from both sides:

\displaystyle -20=5x

\displaystyle \frac{-20}{5}=x

\displaystyle -4=x

Example Question #1 : How To Find X Or Y Intercept

What is the y-intercept of \displaystyle 2y=3x+5?

Possible Answers:

\displaystyle \frac{2}{5}

\displaystyle \frac{10}{3}

\displaystyle 2

\displaystyle \frac{5}{2}

\displaystyle \frac{1}{2}

Correct answer:

\displaystyle \frac{5}{2}

Explanation:

To find the y-intercept, set the x value to zero and solve:

\displaystyle 2y=3x+5

\displaystyle 2y=3(0)+5

\displaystyle 2y=5

\displaystyle y=\frac{5}{2}

Example Question #3 : How To Find X Or Y Intercept

What is the x-intercept of \displaystyle y=\frac{2}{3}x+6?

Possible Answers:

\displaystyle x=6

\displaystyle x=-9

\displaystyle x=9

\displaystyle x=-4

\displaystyle x=0

Correct answer:

\displaystyle x=-9

Explanation:

To solve for the x-intercept, we set the \displaystyle y value equal to \displaystyle 0 and solve.

\displaystyle y=\frac{2}{3}x+6

\displaystyle 0=\frac{2}{3}x+6

\displaystyle -6=\frac{2}{3}x

\displaystyle \frac{3}{2}*-6=x

\displaystyle -9=x

Example Question #2 : Intercepts And Curves

What is the y-intercept of \displaystyle y=\frac{2}{3}x+6?

Possible Answers:

\displaystyle y=6

\displaystyle y=4

\displaystyle y=18

\displaystyle y=-6

\displaystyle y=-9

Correct answer:

\displaystyle y=6

Explanation:

When looking at an equation in standard \displaystyle y=mx+b form, \displaystyle b is our y-intercept.

Or, set the \displaystyle x value equal to \displaystyle 0 and solve.

\displaystyle y=\frac{2}{3}x+6

\displaystyle y=\frac{2}{3}(0)+6

\displaystyle y=6

Example Question #2 : How To Find X Or Y Intercept

What is the y-intercept of \displaystyle 5x+6y=-12

 

Possible Answers:

\displaystyle -10

\displaystyle -4

\displaystyle 2

\displaystyle -2

\displaystyle 4

Correct answer:

\displaystyle -2

Explanation:

Isolate for \displaystyle y so that the equation is in slope-intercept form \displaystyle y=mx+b.

The \displaystyle b is the y-intercept, which in this case, is \displaystyle -2

Example Question #3 : Intercepts And Curves

What are the \displaystyle x-intercepts of \displaystyle y=x^2-6x ?

Possible Answers:

\displaystyle x=-1, -6

\displaystyle x=16

\displaystyle x=0, 6

\displaystyle x=0

\displaystyle x=0, -6

Correct answer:

\displaystyle x=0, 6

Explanation:

Factor out an \displaystyle x from the original equation so that it is \displaystyle x(x-6).

Set that expressions equal to \displaystyle 0 so that you can find the \displaystyle x-intercepts. Your answers are \displaystyle 0 and \displaystyle 6

 

Example Question #73 : Algebra I

Find the \displaystyle x-intercepts of \displaystyle y=3x^2-9x.

Possible Answers:

\displaystyle x=-3, -9

\displaystyle x=3, -3

\displaystyle x=0, 3

\displaystyle x=0, -3

Correct answer:

\displaystyle x=0, 3

Explanation:

Take out a \displaystyle 3x from the original equation so that you can set the expression \displaystyle 3x(x-3) equal to \displaystyle 0 and get your \displaystyle x-intercepts \displaystyle 0 and \displaystyle 3

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