1) Write the equation of the line, in point-slope form, that passes through the points \((-2,3)\) and \((7, -2)\).
2) Write the equation of the line, in slope-intercept form, that passes through the points \((8,-1)\) and \((-4,-4)\).
For Questions 3-4, determine if the lines are parallel, perpendicular, or neither.
3) Line A passes through the points \((-9,-4)\) and \((3,0)\); Line B passes through \((-1,5)\) and \((3,-7)\).
4) Line Q passes through the points \((2, 10)\) and \((-1, -5)\); Line T passes through \((10,3)\) and \((0,1)\).
5) Write the equation of the line, in standard form, that is parallel to the line \(y=2\) and passes through the point \((-5, -13)\).
6) Write the equation of the line, in point-slope form, that is perpendicular to the line \(y-4=-6(x+3)\) and passes through the point \((7, -4)\).
7) Write the equation of the line, in slope-intercept form, that is parallel to the line \(y=3x-1\) and passes through the point \((2,11)\).
8) Write the equation of the line, in slope-intercept form, that is perpendicular to the line \(y=5x+2\) and passes through the point \((-10,1)\).
9) Write the equation of the line, in standard form, that is parallel to \(y=-3x+7\) and passes through the point \((-3,-5)\).
10) Write the equation of the line, in standard form, that is perpendicular to the line \(y=\frac{2}{3}x+9\) and passes through the point \((-6,7)\).
Use a graphing device to complete problems 11-12.
11) Find the linear equation of best fit for the data in the table below. Also find the correlation coefficient and use the equation to predict the y-value when \(x=28\)
2) Write the equation of the line, in slope-intercept form, that passes through the points \((8,-1)\) and \((-4,-4)\).
For Questions 3-4, determine if the lines are parallel, perpendicular, or neither.
3) Line A passes through the points \((-9,-4)\) and \((3,0)\); Line B passes through \((-1,5)\) and \((3,-7)\).
4) Line Q passes through the points \((2, 10)\) and \((-1, -5)\); Line T passes through \((10,3)\) and \((0,1)\).
5) Write the equation of the line, in standard form, that is parallel to the line \(y=2\) and passes through the point \((-5, -13)\).
6) Write the equation of the line, in point-slope form, that is perpendicular to the line \(y-4=-6(x+3)\) and passes through the point \((7, -4)\).
7) Write the equation of the line, in slope-intercept form, that is parallel to the line \(y=3x-1\) and passes through the point \((2,11)\).
8) Write the equation of the line, in slope-intercept form, that is perpendicular to the line \(y=5x+2\) and passes through the point \((-10,1)\).
9) Write the equation of the line, in standard form, that is parallel to \(y=-3x+7\) and passes through the point \((-3,-5)\).
10) Write the equation of the line, in standard form, that is perpendicular to the line \(y=\frac{2}{3}x+9\) and passes through the point \((-6,7)\).
Use a graphing device to complete problems 11-12.
11) Find the linear equation of best fit for the data in the table below. Also find the correlation coefficient and use the equation to predict the y-value when \(x=28\)
\(x\) |
\(11\) |
\(17\) |
\(18\) |
\(25\) |
\(26\) |
\(30\) |
\(33\) |
\(y\) |
\(106\) |
\(114\) |
\(112\) |
\(131\) |
\(128\) |
\(140\) |
\(147\) |
12) The table below shows the attendance at a fall festival. Let \(x\) represent the years since it opened in \(2005\) and \(y\) represent the attendance (in thousands) at the festival. Find the linear equation of best fit, the correlation coefficient, and use it to predict the festival attendance in \(2025\).
\(x\) |
\(2\) |
\(4\) |
\(6\) |
\(8\) |
\(10\) |
\(12\) |
\(y\) |
\(23.5\) |
\(17.4\) |
\(26.6\) |
\(34.2\) |
\(56.9\) |
\(65.1\) |