Chapter 3

A college campus goes beyond the standards described in Exercise \(49 .\) All wheelchair ramps on campus are designed so that every vertical rise of 1 foot is accompanied by a horizontal run of 14 feet. What is the grade of such a ramp? Round to the nearest tenth of a percent.

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned} &y=-2 x+1\\\ &y=2 x+1 \end{aligned}$$

Graph each equation. $$y=-3$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=14 x$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((2,-3)\) and perpendicular to the line whose equation is \(y=\frac{1}{5} x+6\)

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned} &y=x+3\\\ &y=-x+1 \end{aligned}$$

Graph each equation. $$x=2$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-10 x$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-4,2)\) and perpendicular to the line whose equation is \(y=\frac{1}{3} x+7\)

Describe how to calculate the slope of a line passing through two points.

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned} &y=x+2\\\ &y=-x-1 \end{aligned}$$

Graph each equation. $$x=4$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-20 x$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,2)\) and parallel to the line whose equation is \(2 x-3 y=7\)

What does it mean if the slope of a line is zero?

Graph each equation. $$x+1=0$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=8 x-5$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-1,3)\) and parallel to the line whose equation is \(3 x-2 y=5\)

What does it mean if the slope of a line is undefined?

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{array}{r} x-3 y=9 \\ 3 x-9 y=18 \end{array}$$

Graph each equation. $$x+5=0$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=6 x-4$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((4,-7)\) and perpendicular to the line whose equation is \(x-2 y=3\)

If two lines are parallel, describe the relationship between their slopes.

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{array}{r} 2 x-y=-1 \\ x+2 y=-6 \end{array}$$

Graph each equation. $$y-3.5=0$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-3 x+7$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((5,-9)\) and perpendicular to the line whose equation is \(x+7 y=12\)

If two lines are perpendicular, describe the relationship between their slopes.

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{array}{r} 3 x-y=-2 \\ x+3 y=-9 \end{array}$$

Graph each equation. $$y-2.5=0$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-5 x+9$$

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((2,4)\) and has the same \(y\) -intercept as the line whose equation is \(x-4 y=8\)

When finding the slope of the line passing through \((-1,5)\) and \((2,-3),\) I must let \(\left(x_{1}, y_{1}\right)\) be \((-1,5)\) and \(\left(x_{2}, y_{2}\right)\) be \((2,-3)\).

In Exercises \(57-64\), write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is 5 and the line is parallel to the line whose equation is \(3 x+y=6\)

Graph each equation. $$x=0$$

Graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x$$

The line passes through \((2,4)\) and has the same \(y\) -intercept as the line whose equation is \(x-4 y=8\) The line passes through \((2,6)\) and has the same \(y\) -intercept as the line whose equation is \(x-3 y=18\)

In Exercises \(57-64\), write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is \(-4\) and the line is parallel to the line whose equation is \(2 x+y=8\)

Graph each equation. $$y=0$$

Graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x+1$$

Write an equation in slope-intercept form of the line satisfying the given conditions. The line has an \(x\) -intercept at \(-4\) and is parallel to the line containing \((3,1)\) and \((2,6)\)

In Exercises \(57-64\), write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is 6 and the line is perpendicular to the line -whose equation is \(y=5 x-1\)

Graph each equation. $$3 y=9$$

Graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x-1$$

Write an equation in slope-intercept form of the line satisfying the given conditions. The line has an \(x\) -intercept at \(-6\) and is parallel to the line containing \((4,-3)\) and \((2,2)\)

I computed the slope of one line to be \(-\frac{3}{5}\) and the slope of a second line to be \(-\frac{5}{3},\) so the lines must be perpendicular.

In Exercises \(57-64\), write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is 7 and the line is perpendicular to the line whose equation is \(y=8 x-3\)

Graph each equation. $$5 y=20$$

Graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x-2$$