Chapter 3

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$2 x+3 y=30$$

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(l_{1}\) goes through \((3,6)\) and \((4,9), l_{2}\) goes through \((5,3)\) and \((6,0)\)

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$y=2 x-4$$

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. In goes through \((0,2)\) and \((7,9), l_{2}\) goes through \((0,-3)\) and \((1,-2)\)

Find an equation of the line that goes through the given point and has the given slope. Give the answer in slope-intercept form. See Example 5 (-3, -1) with slope 6

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$y=-3 x+6$$

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(l_{1}\) goes through \((4,3)\) and \((2,6), l_{2}\) goes through \((0,0)\) and \((3,2)\)

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$y=-\frac{1}{2} x-20$$

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(l_{1}\) goes through \((0,0)\) and \((-2,5), l_{2}\) goes through \((0,1)\) and \((2,6)\)

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$y=\frac{1}{3} x+10$$

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(l_{1}\) goes through \((0,3)\) and \((4,17), l_{2}\) goes through \((-1,-4)\) and \((1,3)\)

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(l_{1}\) goes through \((-2,-3)\) and \((4,1), l_{2}\) goes through \((-1,7)\) and \((1,4)\)

Find an equation of the line that goes through the given point and has the given slope. Give the answer in slope-intercept form. See Example 5 (-9, -4) with slope 0

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts. $$y=2-3 x$$

Solve each geometric figure problem. If the opposite sides of a quadrilateral are parallel, then it is a parallelogram. Use slope to determine whether the points \((-6,1),(-2,-1),(0,3),\) and \((4,1)\) are the vertices of a parallelogram.

Find an equation of the line that goes through the given point and has the given slope. Give the answer in slope-intercept form. See Example 5 (-5, 150) with slope -30

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts. $$y=800 x+8$$

Solve each geometric figure problem. A trapezoid is a quadrilateral with one pair of parallel sides. Use slope to determine whether the points \((-3,2)\) \(-(-1,-1),(3,6),\) and \((6,4)\) are the vertices of a trapezoid.

Solve each geometric figure problem. If a triangle has one right angle, then it is a right triangle. Use slope to determine whether the points \((-3,3),(-1,6)\) and \((0,0)\) are the vertices of a right triangle.

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts. $$y=30.6-3.6 x$$

Solve each geometric figure problem. Use slope to determine whether the points \((0,-1),(2,5)\) and \((5,4)\) are the vertices of a right triangle.

Find all intercepts for each line. Some of these lines have only one intercept. $$x+y=50$$

Find all intercepts for each line. Some of these lines have only one intercept. $$x+2 y=100$$

Find all intercepts for each line. Some of these lines have only one intercept. $$3 x-5 y=15$$

If a line passes through \((5,2)\) and has slope \(\frac{2}{3},\) then what is the value of \(y\) on this line when \(x=8, x=11,\) and \(x=12 ?\) cant copy the graph

Find all intercepts for each line. Some of these lines have only one intercept. $$9 x+8 y=72$$

Find \(k\) so that the line through \((2, k)\) and \((-3,-5)\) has slope \(\frac{1}{2}\)

Find all intercepts for each line. Some of these lines have only one intercept. $$y=5 x$$

Find \(k\) so that the line through \((k, 3)\) and \((-2,0)\) has slope 3

Find all intercepts for each line. Some of these lines have only one intercept. $$y=-4 x$$

What is the slope of a line that is perpendicular to a line with slope \(0.247 ?\)

Find all intercepts for each line. Some of these lines have only one intercept. $$6 x+3=0$$

What is the slope of a line that is perpendicular to the line through \((3.27,-1.46)\) and \((-5.48,3.61) ?\)

Find all intercepts for each line. Some of these lines have only one intercept. $$12+18 y=0$$

Is it possible for a line to be in only one quadrant? Two quadrants? Write a rule for determining whether a line has positive, negative, zero, or undefined slope from knowing in which quadrants the line is found.

Find all intercepts for each line. Some of these lines have only one intercept. $$2-10 y=0$$

Find the equation of line \(l\). Write the answer in standard form with integral coefficient with a positive coefficient for \(x .\) See Example 8. Line \(l\) goes through \((3,2)\) and is perpendicular to \(3 x-12 y=1\).

A rhombus is a quadrilateral with four equal sides. Draw a rhombus with vertices \((-3,-1),(0,3),(2,-1)\) and \((5,3) .\) Find the slopes of the diagonals of the rhombus. What can you conclude about the diagonals of this rhombus?

Find the equation of line \(l\). Write the answer in standard form with integral coefficient with a positive coefficient for \(x .\) See Example 8. Line \(l\) goes through \((-2,5)\) and is perpendicular to \(6 x+3 y=7\)

Find all intercepts for each line. Some of these lines have only one intercept. $$9 x+3=12 y$$

Find the equation of line \(l\). Write the answer in standard form with integral coefficient with a positive coefficient for \(x .\) See Example 8. Line \(l\) goes through \((4,-2)\) and is parallel to \(4 x+2 y=5\).

Graph \(y=1 x, y=2 x, y=3 x,\) and \(y=4 x\) together in the standard viewing window. These equations are all of the form \(y=m x .\) What effect does increasing \(m\) have on the graph of the equation? What are the slopes of these four lines?

Complete the given ordered pairs so that each ordered pair satisfies the given equation. $$(2, \quad),(\quad,-3), \quad y=-3 x+6$$

Find the equation of line \(l\). Write the answer in standard form with integral coefficient with a positive coefficient for \(x .\) See Example 8. Line \(l\) goes through \((-6,2)\) and is parallel to \(3 x-9 y=7\).

Graph \(y=-1 x, y=-2 x, y=-3 x,\) and \(y=-4 x\) together in the standard viewing window. These equations are all of the form \(y=m x\). What effect does decreasing \(m\) have on the graph of the equation? What are the slopes of these four lines?

Complete the given ordered pairs so that each ordered pair satisfies the given equation. $$(-1,\quad),(\quad, 4), \quad y=\frac{1}{2} x+2$$

Find the equation of line l in each case and then write it in standard form with integral coefficients. Line \(l\) has slope \(\frac{1}{2}\) and goes through \((0,5)\).

Complete the given ordered pairs so that each ordered pair satisfies the given equation. $$ (-4,\quad),(\quad, 6),\quad \frac{1}{2} x-\frac{1}{3} y=9 $$

Find the equation of line l in each case and then write it in standard form with integral coefficients. Line \(l\) has slope 5 and goes through \(\left(0, \frac{1}{2}\right)\).

Find the equation of line l in each case and then write it in standard form with integral coefficients. Line \(l\) has \(x\) -intercept \((2,0)\) and \(y\) -intercept \((0,4)\).