Chapter ISG, Problem 4.2.1P

a.

To determine

To calculate slope, x y intersects and point

Answer to Problem 4.2.1P

The slope is $\frac{1}{3}$ , point is $(5,-4)$ , y-intercept is $-\frac{17}{3}$ and x-intercept is $17$ .

Explanation of Solution

Given information:

  $y+4=\frac{1}{3}(x-5)$

Formula Used:

Equation of line is,

  $y-y1=m(x-x1)$

and

  $y=mx+c$

Graph:

  

Calculation:

Comparing the given equation and equation of line in terms of point and slope,

Slope of the line is,

  $\frac{1}{3}$

Point it passes through is,

  $(5,-4)$

Opening the brackets of the given equation,

  $y+4=\frac{1}{3}x-\frac{5}{3}$

Shifting left-hand side values to right hand side,

  $y=\frac{1}{3}x-\frac{5}{3}-4$

On solving,

  $y=\frac{1}{3}x-\frac{17}{3}$ ____________________(1)

Comparing it with the equation of line in terms of slope and intercept,

y- intercept is,

  $-\frac{17}{3}$

Shifting the right hand side values to left hand side on equation (1),

  $\frac{1}{3}x=y+\frac{17}{3}$

Cross-multiplying both sides,

  $x=3(y+\frac{17}{3})$

On solving,

  $x=3y+17$

Comparing it with the equation of line in terms of slope and intercept,

x- intercept is,

  $17$

Conclusion:The slope is $\frac{1}{3}$ , point is $(5,-4)$ , y-intercept is $-\frac{17}{3}$ and x-intercept is $17$ .

b.

To determine

To calculate slope, x y intersects and point

Answer to Problem 4.2.1P

The slope is 2.5, point is $(-8,2)$ , x-intercept is 7.2 and y- intercept is -18.

Explanation of Solution

Given information:

  $y-2=-2.5(x+8)$

Formula Used:

Equation of line is,

  $y-y1=m(x-x1)$

and

  $y=mx+c$

Graph:

  

Calculation:

Comparing the given equation and equation of line in terms of point and slope,

Slope of the line is,

  $-2.5$

Point it passes through is,

  $(-8,2)$

Opening the brackets of the given equation,

  $y-2=-2.5x-20$

Shifting left-hand side values to right hand side,

  $y=-2.5x-20+2$

On solving,

  $y=-2.5x-18$ ____________________(1)

Comparing it with the equation of line in terms of slope and intercept,

y- intercept is,

  $-18$

Shifting the right hand side values to left hand side on equation (1),

  $-2.5x=-y-18$

Cross-multiplying both sides,

  $x=\frac{-1}{2.5}(-y-18)$

On solving,

  $x=\frac{1}{2.5}y+7.2$

Comparing it with the equation of line in terms of slope and intercept,

x- intercept is,

  $7.2$

Conclusion:The slope is 2.5, point is $(-8,2)$ , x-intercept is 7.2 and y- intercept is -18.