Chapter 5

Perpendicular lines intersect at a ____ ? angle.

Name the following form of an equation of a line: \(y=m x+b .\) What does \(m\) represent? What does \(b\) represent?

When writing an equation of a line given two points, which form should you use if you do not know the \(y\) -intercept?

What is the name used to describe an equation in the form \(y=m x+b ?\)

Two lines are perpendicular. If the slope of one of the lines is \(-\frac{5}{7},\) then what the slope of the other line?

Name the following form of an equation of a line: \(A x+B y=C .\) Give an example of an equation in this form.

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (2,-1), m=3 $$

Identify the slope of the line that has the equation \(y=-4 x+15\)

Determine whether the lines are perpendicular. $$ y=\frac{1}{5} x-3, y=-5 x+3 $$

Write the equation in standard form with integer coefficients. \(y=2 x-9\)

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (3,4), m=4 $$

Name the \(y\) -intercept of the line that has the equation \(y=10 x-3\)

Determine whether the lines are perpendicular. $$ y=-4 x+8, y=\frac{1}{4} x+7 $$

Write the equation in standard form with integer coefficients. \(y=\frac{1}{2} x+8\)

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (-5,-7), m=-2 $$

Determine whether the equation is in slope-intercept form. $$ y=-8 x-11 $$

Determine whether the lines are perpendicular. $$ y=\frac{3}{8} x+1, y=\frac{8}{3} x-2 $$

Determine whether the equation is in slope-intercept form. $$ y-4=5(x+3) $$

Between the years of 1990 and 2000 dollars the annual profit for the Alpha Company increased by about 70,000 dollars per year. In 1998 dollars the company had an annual profit of 2,000,000 dollars. Write the equation in slope intercept form that gives the annual profit \(P\) for the Alpha Company in terms of \(t .\) Let \(t=0\) represent the year 1990 dollars.

Determine whether the lines are perpendicular. $$ y=3, x=4 $$

Write in standard form an equation of the line that passes through the given point and has the given slope. Use integer coefficients. \((3,4), m=-4\)

Determine whether the equation is in slope-intercept form. $$ x+23 y=-15 $$

Write in slope-intercept form the equation of the line that passes through the given points. $$ (-1,1) \text { and }(2,5) $$

In Exercises \(7-11\), a mountain climber is scaling a 400 -foot cliff. The climber starts at the bottom at \(t=0\) and climbs at a constant rate of 124 feet per hour. What is the slope in the linear model for the situation?

Write the equation of the line passing through the two points. Show that this line is perpendicular to the given line. $$ (-3,0),(3,6) ; y=-x-2 $$

Write in standard form an equation of the line that passes through the given point and has the given slope. Use integer coefficients. \((1,-2), m=5\)

Write in slope-intercept form the equation of the line described below. Slope \(=1, y\) -intercept \(=0\)

In Exercises \(7-11\), a mountain climber is scaling a 400 -foot cliff. The climber starts at the bottom at \(t=0\) and climbs at a constant rate of 124 feet per hour. The \(y\) -intercept represents the height at which the climber begins scaling the cliff. What is the \(y\) -intercept in the linear model?

Write in slope-intercept form the equation of the line that passes through the given points. $$ (4,3) \text { and }(1,6) $$

Write the equation of the line passing through the two points. Show that this line is perpendicular to the given line. $$ (-4,-4),(-2,2) ; y=-\frac{1}{3} x-1 $$

Write in standard form an equation of the line that passes through the given point and has the given slope. Use integer coefficients. \((-2,-5), m=3\)

In Exercises \(7-11\), a mountain climber is scaling a 400 -foot cliff. The climber starts at the bottom at \(t=0\) and climbs at a constant rate of 124 feet per hour. Use the slope and \(y\) -intercept to write the linear model for the distance \(y\) (in feet) that the climber climbs in terms of time \(t\) (in hours). Use slope intercept form.

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. $$ (-1,-3), m=\frac{1}{2} $$

Write the equation of the line passing through the point and perpendicular to the given line. $$ (5,2), y=-\frac{1}{2} x+4 $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((3,1),(4,-2)\)

Write in point-slope form the equation of the line that passes through the given points. $$ (2,3) \text { and }(0,4) $$

In Exercises \(7-11\), a mountain climber is scaling a 400 -foot cliff. The climber starts at the bottom at \(t=0\) and climbs at a constant rate of 124 feet per hour. After 3 hours, has the climber reached the top of the cliff?

Write the equation of the line passing through the point and perpendicular to the given line. $$ (6,0), y=-2 x+7 $$

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. $$ (2,-3), m=0 $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((1,6),(1,-5)\)

Write in point-slope form the equation of the line that passes through the given points. $$ (0,0) \text { and }(-6,-5) $$

Write in point-slope form the equation of the line that passes through the given points. $$ (0,-10) \text { and }(12,4) $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((5,0),(0,3)\)

Write in slope-intercept form the equation of the line described below. Slope \(=5, y\) -intercept \(=5\)

In Exercises \(12-17\), use the following information. Renting a canoe costs 10 dollars plus 28 dollars per day. The linear model for this situation relates the total cost of renting a canoe, \(y,\) with the number of days rented, \(x\). What number corresponds to the slope in the linear model?

Determine whether the lines are perpendicular. $$ y=-\frac{1}{3} x+1, y=-3 x+3 $$

Write in point-slope form the equation of the line that passes through the given points. $$ (0,9) \text { and }(8,7) $$

Write in slope-intercept form the equation of the line described below. Slope \(=14, y\) -intercept \(=-6\)

In Exercises \(12-17\), use the following information. Renting a canoe costs 10 dollars plus 28 dollars per day. The linear model for this situation relates the total cost of renting a canoe, \(y,\) with the number of days rented, \(x\). What number corresponds to the \(y\) -intercept in the linear model?

Determine whether the lines are perpendicular. $$ y=\frac{1}{2} x-7, y=-2 x $$