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Virtual Math Learning Center

Virtual Math Learning Center Texas A&M University Virtual Math Learning Center

Section 2.1 – Review of Lines

Exercises

Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.

1. Determine the slope of the line passing through the following points given below.

  1. \((−3, −7)\) and \((5, −2)\)
  2. \(\left(−\dfrac{3}{4},2\right)\) and \(\left(-\dfrac{3}{4},5\right)\)
  3. \(\left(\dfrac{1}{2},\dfrac{3}{5}\right)\) and \(\left(-\dfrac{1}{2},\dfrac{3}{5}\right)\)

  1. \(\dfrac{5}{8}\)
  2. Undefined
  3. \(0\)

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2. Write the equation of the line which passes through \((4,12)\) and \((−5,6)\) in point-slope form, slope-intercept form, and standard form.​

  1. Point-Slope: \(y-12=\dfrac{2}{3}(x-4)\)
  2. Slope-Intercept: \(y=\dfrac{2}{3}x+\dfrac{28}{3}\)
  3. Standard Form: \(-2x+3y=28\)

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3. Write the equation of the line which passes through \((−2, 31)\) and has an undefined slope in point-slope form, slope-intercept form, and standard form.​

  1. Point-Slope: Not Possible
  2. Slope-Intercept: Not Possible
  3. Standard Form: \(x=-2\)

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4. Write the equation of the line which passes through \((−2, 31)\) and has a slope of zero in point-slope form, slope-intercept form, and standard form.

  1. Point-Slope: \(y-31=0(x+2)\)
  2. Slope-Intercept: \(y=31\)
  3. Standard Form: \(y=31\)

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5. Determine, without the aid of a graphing calculator, the x- and y-intercepts for \(5x−8y = 13.\)

  1. \(x\)-intercept: \(\left( \dfrac{13}{5},0\right) \)
  2. \(y\)-intercept: \(\left(0,-\dfrac{13}{8}\right)\)

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6. Given \(C\) is an integer, find the value of \(C\) so the line given by \(14x+8y = C\) has an \(x\)-intercept of \((4, 0).\)

\(C=56\)

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7. Without the use of technology, graph the line \(y=-\dfrac{3}{5}(x-1)+4.\)

See the video for the graph

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8. Without the use of technology, graph the line \(y=\dfrac{5}{2}x-3.\)

See the video for the graph

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9. Without the use of technology, graph the line \(x=5.\)

See the video for the graph.

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10. Given the line \(5x − 11y = 2\), if \(x\) increases by \(7\) units, what is the corresponding change in \(y?\)

\(y\) will increase by \(\dfrac{35}{11}\)

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11. Given the line \(5x − 11y = 2\), if \(y\) decreases by \(32\) units, what is the corresponding change in \(x?\)

\(x\) will decrease by \(70.4\) units.

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12. Determine the slope of the line passing through the points \((a, −3)\) and \((5, 3a)\), in terms of \(a\). For what value(s) of \(a\) is the slope of the line undefined?

The slope is \(\dfrac{3a+3}{5-a}.\)
The slope is undefined when \(a=5.\)

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