Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #143 : How To Find Slope Of A Line

Find the slope of the coordinates.

\displaystyle (-5.5,6.4)(-3.2,-0.5)

Possible Answers:

\displaystyle \frac{23}{29}

\displaystyle -\frac{1}{3}

\displaystyle \frac{1}{3}

\displaystyle -3

\displaystyle -\frac{59}{29}

Correct answer:

\displaystyle -3

Explanation:

To find slope, it is differences of the \displaystyle y-coordinates divided by the differences of the \displaystyle x-coordinates.

\displaystyle \frac{6.4-(-0.5)}{-5.5-(-3.2)}=\frac{6.9}{-2.3}=-3

Example Question #551 : Functions And Lines

Find the slope of the coordinates.

\displaystyle (-8,4)(-8,3)

Possible Answers:

\displaystyle -1

\displaystyle 1

\displaystyle 0

\displaystyle 7

\displaystyle \infty

Correct answer:

\displaystyle \infty

Explanation:

Anytime you see two \displaystyle x-coordinates that are the same, this means the slope is vertical. When slopes are vertical, that means the slope is infinity.

Example Question #552 : Functions And Lines

Find the slope of the coordinates.

\displaystyle (-12,7)(24,7)

Possible Answers:

\displaystyle 0

\displaystyle \infty

\displaystyle 2

\displaystyle -1

\displaystyle 1

Correct answer:

\displaystyle 0

Explanation:

Anytime you see the \displaystyle y-coordinates the same, that means the slope is just a horizontal line. When slopes are horizontal lines, the slope is \displaystyle 0.

Example Question #143 : How To Find Slope Of A Line

Find the slope with the given equation.

\displaystyle y=4x+5

Possible Answers:

\displaystyle 4

\displaystyle 9

\displaystyle 5

\displaystyle 1

\displaystyle 20

Correct answer:

\displaystyle 4

Explanation:

The equation of a slope is \displaystyle y=mx+b\displaystyle m is the slope while \displaystyle b is the \displaystyle y-intercept. So, \displaystyle m in this case is \displaystyle 4. The slope value will always be the coefficient of \displaystyle x.

Example Question #143 : How To Find Slope Of A Line

Find the slope with the given equation.

\displaystyle y=-3-6x

Possible Answers:

\displaystyle -6

\displaystyle -9

\displaystyle 3

\displaystyle 18

\displaystyle -3

Correct answer:

\displaystyle -6

Explanation:

The equation of a slope is \displaystyle y=mx+b\displaystyle m is the slope while \displaystyle b is the \displaystyle y-intercept. So, \displaystyle m in this case is \displaystyle -6. The slope value will always be the coefficient of \displaystyle x.

Example Question #143 : How To Find Slope Of A Line

Find the slope with the given equation.

\displaystyle 3y+5x=10

Possible Answers:

\displaystyle 3

\displaystyle \frac{10}{3}

\displaystyle 5

\displaystyle -\frac{5}{3}

\displaystyle \frac{3}{10}

Correct answer:

\displaystyle -\frac{5}{3}

Explanation:

The equation of a slope is \displaystyle y=mx+b\displaystyle m is the slope while \displaystyle b is the \displaystyle y-intercept. We need to solve for \displaystyle y

\displaystyle 3y+5x=10 Subtract \displaystyle 5x on both sides. 

\displaystyle 3y=10-5x Divide \displaystyle 3 on both sides.

So, \displaystyle m in this case is \displaystyle -\frac{5}{3}. The slope value will always be the coefficient of \displaystyle x.

Example Question #551 : Functions And Lines

Find the slope with the given equation.

\displaystyle 12+5y=6x

Possible Answers:

\displaystyle \frac{6}{5}

\displaystyle 5

\displaystyle 6

\displaystyle -\frac{12}{5}

\displaystyle 12

Correct answer:

\displaystyle \frac{6}{5}

Explanation:

The equation of a slope is \displaystyle y=mx+b\displaystyle m is the slope while \displaystyle b is the \displaystyle y-intercept. We need to solve for \displaystyle y

\displaystyle 12+5y=6x Subtract \displaystyle 12 on both sides. 

\displaystyle 5y=6x-12 Divide \displaystyle 6 on both sides.

So, \displaystyle m in this case is \displaystyle \frac{6}{5}. The slope value will always be the coefficient of \displaystyle x.

Example Question #552 : Functions And Lines

Find the slope with the given equation.

\displaystyle y=x

Possible Answers:

\displaystyle 1

\displaystyle 2

\displaystyle 0

\displaystyle -2

\displaystyle -1

Correct answer:

\displaystyle 1

Explanation:

The equation of a slope is \displaystyle y=mx+b\displaystyle m is the slope while \displaystyle b is the \displaystyle y-intercept. So, \displaystyle m in this case is \displaystyle 1. The slope value will always be the coefficient of \displaystyle x.

Example Question #553 : Functions And Lines

Find the slope with the given equation.

\displaystyle x=5

Possible Answers:

\displaystyle 5

\displaystyle \frac{1}{5}

\displaystyle \infty

\displaystyle 1

\displaystyle 0

Correct answer:

\displaystyle \infty

Explanation:

The equation of a slope is \displaystyle y=mx+b\displaystyle m is the slope while \displaystyle b is the \displaystyle y-intercept. Problem is we don't have a \displaystyle y. This means the graph will be a vertical line with the line crossing through the \displaystyle x-axis at \displaystyle 5. Vertical slopes mean the slope is infinity.

 

Example Question #554 : Functions And Lines

What is the slope of a line with the equation  \displaystyle y=9x+8?

Possible Answers:

\displaystyle -1

\displaystyle \frac{9}{8}

\displaystyle \frac{8}{9}

\displaystyle 9

\displaystyle 8

Correct answer:

\displaystyle 9

Explanation:

The current equation is already in the slope intercept form.

The slope-intercept form is:

\displaystyle y=mx+b

The \displaystyle m is the slope of the equation.

The answer is \displaystyle 9.

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