This page contains practice questions on slopes and equations of straight lines. Topics include slope calculation, vertical and horizontal lines, slope–intercept form, parallel and perpendicular lines, and systems of linear equations. Complete answers are provided at the end of the page.
Find, if possible, the slope of the line through the points \((\tfrac{1}{2}, \tfrac{3}{4})\) and \((-\tfrac{1}{3}, \tfrac{5}{4})\).
Find, if possible, the slope of the line through the points \((2, 5)\) and \((-4, 5)\).
Find, if possible, the slope of the line through the points \((-9, 4)\) and \(-9, -2)\).
Line \(L\) passes through the points \((4, -5)\) and \((3, 7)\). Find the slope of any line perpendicular to line \(L\).
Find the slope of the line given by the equation \[ 2x + 4y = 10. \]
Write an equation, in slope–intercept form, of the line passing through the points \((2, 3)\) and \((4, 6)\).
Write an equation, in slope–intercept form, of the line with an \(x\)-intercept at \((3, 0)\) and a \(y\)-intercept at \((0, -5)\).
Write an equation, in slope–intercept form, of the line with slope \(-2\) and passing through the point \((-4, -5)\).
Write an equation of the vertical line passing through the point \((3, 0)\).
Write an equation of the horizontal line passing through the point \((7, -5)\).
Find an equation of the line passing through the points \((-3, 5)\) and \((9, 10)\). Write your answer in the standard form \[ Ax + By = C, \quad A > 0. \]
Find an equation of the line parallel to \[ 3x + 6y = 5 \] and passing through the point \((1, 3)\). Write the equation in slope–intercept form.
Find an equation of the line perpendicular to \[ 3x + 6y = 5 \] and passing through the point \((1, 3)\). Write the equation in standard form.
Write the equation of the line parallel to the line \(x = 5\) and passing through the point \((3, -10)\).
Write the equation of the line perpendicular to the line \(x = 2\) and passing through the point \((2, -8)\).
Write the equation of the line passing through the midpoint of the line segment with endpoints \((2, 8)\) and \((0, 4)\), and perpendicular to the line \[ -3x + 6y = 5. \]
Determine whether the lines \[ 2x - 3y = 8 \quad \text{and} \quad -x + 4y = 2 \] are parallel, perpendicular, or neither.
Determine whether the lines \[ 2x = 8 \quad \text{and} \quad -3y = 15 \] are parallel, perpendicular, or neither.
Find the point of intersection of the lines \[ x = 7 \quad \text{and} \quad y = -9. \]
Rewrite the equation \[ |y| = |x| \] as two equations representing two straight lines.
1) \(-\tfrac{3}{5}\)
2) \(0\)
3) Undefined
4) \(\tfrac{1}{12}\)
5) \(-\tfrac{1}{2}\)
6) \(y = \tfrac{3}{2}x\)
7) \(y = \tfrac{5}{3}x - 5\)
8) \(y = -2x - 13\)
9) \(x = 3\)
10) \(y = -5\)
11) \(5x - 12y = -75\)
12) \(y = -\tfrac{1}{2}x + \tfrac{7}{2}\)
13) \(y = 2x + 1\)
14) \(x = 3\)
15) \(y = -8\)
16) \(y = -2x + 8\)
17) Neither
18) Perpendicular
19) \((7, -9)\)
20) \(y = x\) and \(y = -x\)