Chapter 3

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \((-2,-4)\) and \((1,-1)\)

Begin by solving the linear equation for \(y .\) This will put the equation in slope-intercept form. Then find the slope and the \(y\) -intercept of the line with this equation. $$3 y=-9 x$$

Graph each inequality. $$5 x-y<-7$$

plot the given point in a rectangular coordinate system. $$(0,0)$$

Use intercepts and a checkpoint to graph equation. \(x+3 y=6\)

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \((-4,-1)\) and \((3,4)\)

Begin by solving the linear equation for \(y .\) This will put the equation in slope-intercept form. Then find the slope and the \(y\) -intercept of the line with this equation. $$2 x+7 y=0$$

Graph each inequality. $$x-5 y<-7$$

plot the given point in a rectangular coordinate system. $$\left(-\frac{5}{2}, 0\right)$$

Use intercepts and a checkpoint to graph equation. \(2 x+y=4\)

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \((-6,1)\) and \((2,-5)\)

Begin by solving the linear equation for \(y .\) This will put the equation in slope-intercept form. Then find the slope and the \(y\) -intercept of the line with this equation. $$2 x+9 y=0$$

Graph each inequality. $$y \leq \frac{1}{3} x$$

plot the given point in a rectangular coordinate system. $$\left(0,-\frac{5}{2}\right)$$

Use intercepts and a checkpoint to graph equation. \(6 x-9 y=18\)

In Exercises \(23-26,\) determine whether the distinct lines through each pair of points are parallel. $$(-2,0) \text { and }(0,6) ;(1,8) \text { and }(0,5)$$

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \((-3,-1)\) and \((4,-1)\)

Begin by solving the linear equation for \(y .\) This will put the equation in slope-intercept form. Then find the slope and the \(y\) -intercept of the line with this equation. $$3 x+2 y=3$$

Graph each inequality. $$y \leq \frac{1}{4} x$$

plot the given point in a rectangular coordinate system. $$\left(0, \frac{7}{2}\right)$$

Use intercepts and a checkpoint to graph equation. \(6 x-2 y=12\)

In Exercises \(23-26,\) determine whether the distinct lines through each pair of points are parallel. $$(2,4) \text { and }(6,1) ;(-3,1) \text { and }(1,-2)$$

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \((-2,-5)\) and \((6,-5)\)

Begin by solving the linear equation for \(y .\) This will put the equation in slope-intercept form. Then find the slope and the \(y\) -intercept of the line with this equation. $$4 x+3 y=4$$

Graph each inequality. $$y>2 x$$

Use intercepts and a checkpoint to graph equation. \(-x+4 y=6\)

In Exercises \(23-26,\) determine whether the distinct lines through each pair of points are parallel. \((0,3)\) and \((1,5) ;(-1,7)\) and \((1,10)\)

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \((2,4)\) with \(x\) -intercept \(=-2\)

Begin by solving the linear equation for \(y .\) This will put the equation in slope-intercept form. Then find the slope and the \(y\) -intercept of the line with this equation. $$3 x-4 y=12$$

Graph each inequality. $$y>4 x$$

Use intercepts and a checkpoint to graph equation. \(-x+3 y=10\)

In Exercises \(23-26,\) determine whether the distinct lines through each pair of points are parallel. $$(-7,6) \text { and }(0,4) ;(-9,-3) \text { and }(1,5)$$

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \((1,-3)\) with \(x\) -intercept \(=-1\)

Begin by solving the linear equation for \(y .\) This will put the equation in slope-intercept form. Then find the slope and the \(y\) -intercept of the line with this equation. $$5 x-2 y=10$$

Graph each inequality. $$y>3 x+2$$

Use intercepts and a checkpoint to graph equation. \(2 x-y=7\)

In Exercises \(27-30\), determine whether the lines through each pair of points are perpendicular. \((1,5)\) and \((0,3) ;(-2,8)\) and \((2,6)\)

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. \(x\) -intercept \(=-\frac{1}{2}\) and \(y\) -intercept \(=4\)

Graph each linear equation using the slope and y-intercept. $$y=2 x+4$$

Graph each inequality. $$y>2 x-1$$

Use intercepts and a checkpoint to graph equation. \(2 x-y=5\)

In Exercises \(27-30\), determine whether the lines through each pair of points are perpendicular. \((3,2)\) and \((-2,-2) ;(3,-2)\) and \((-1,3)\)

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. \(x\) -intercept \(=4\) and \(y\) -intercept \(=-2\)

Graph each linear equation using the slope and y-intercept. $$y=3 x+1$$

Graph each inequality. $$y<\frac{3}{4} x-3$$

Use intercepts and a checkpoint to graph equation. \(3 x=5 y-15\)

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((-3,2)\) and is parallel to the line whose equation is \(y=4 x+1.\)

In Exercises \(27-30\), determine whether the lines through each pair of points are perpendicular. $$(-1,-6) \text { and }(2,9) ;(-15,-1) \text { and }(5,3)$$

Graph each linear equation using the slope and y-intercept. $$y=-3 x+5$$

Graph each inequality. $$y<\frac{2}{3} x-1$$