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.
- \((−3, −7)\) and \((5, −2)\)
- \(\left(−\dfrac{3}{4},2\right)\) and \(\left(-\dfrac{3}{4},5\right)\)
- \(\left(\dfrac{1}{2},\dfrac{3}{5}\right)\) and \(\left(-\dfrac{1}{2},\dfrac{3}{5}\right)\)
- \(\dfrac{5}{8}\)
- Undefined
- \(0\)
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.
- Point-Slope: \(y-12=\dfrac{2}{3}(x-4)\)
- Slope-Intercept: \(y=\dfrac{2}{3}x+\dfrac{28}{3}\)
- Standard Form: \(-2x+3y=28\)
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.
- Point-Slope: Not Possible
- Slope-Intercept: Not Possible
- Standard Form: \(x=-2\)
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.
- Point-Slope: \(y-31=0(x+2)\)
- Slope-Intercept: \(y=31\)
- Standard Form: \(y=31\)
5. Determine, without the aid of a graphing calculator, the x- and y-intercepts for \(5x−8y = 13.\)
- \(x\)-intercept: \(\left( \dfrac{13}{5},0\right) \)
- \(y\)-intercept: \(\left(0,-\dfrac{13}{8}\right)\)
6. Given \(C\) is an integer, find the value of \(C\) so the line given by \(14x+8y = C\) has an \(x\)-intercept of \((4, 0).\)
7. Without the use of technology, graph the line \(y=-\dfrac{3}{5}(x-1)+4.\)
8. Without the use of technology, graph the line \(y=\dfrac{5}{2}x-3.\)
9. Without the use of technology, graph the line \(x=5.\)
10. Given the line \(5x − 11y = 2\), if \(x\) increases by \(7\) units, what is the corresponding change in \(y?\)
11. Given the line \(5x − 11y = 2\), if \(y\) decreases by \(32\) units, what is the corresponding change in \(x?\)
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 undefined when \(a=5.\)