Question

Give the slope and y-intercept for each of the lines graphed in Exercise 11.1.

Short answer

1. Slope = 1, y-intercept = 0
2. Slope = -1, y-intercept = 3
3. Slope = 1/5, y-intercept = 6/5
4. Slope = 9/8, y-intercept = 15/4

Step-by-step solution

Introduction

A line's slope is defined as the ratio of the vertical change in y to the horizontal change in x between any two locations on the line. It denotes the direction of a line's slant as well as its steepness.

Give the slope and y-intercept (1, 1) and (5, 5)

Let, A = (1,1) and B = (5,5).

Slope = (y₂-y₁)/(x₂-x₁)

=(5-1)/(5-1)

=4/4

=1

Equation of AB bar is:

y-y₁= m(x-x₁)

y-1 = 1(x-1)

y-1 = x-1

y=x

Therefore, slope = 1, y-intercept = 0.

Give the slope and y-intercept (0, 3) and (3, 0).

Let, A = (0,3) and B = (3,0).

Slope = (y₂-y₁)/(x₂-x₁)

=(0-3)/(3-0)

=-3/3

= -1

Equation of AB bar is:

y-y₁= m(x-x₁)

y-3 = -1(x-0)

y-3= -x

y= -x+3

Therefore, slope = -1, y-intercept = 3.

Give the slope and y-intercept (-1, 1) and (4, 2).

Let, A = (-1,1) and B = (4,2).

Slope = (y₂-y₁)/(x₂-x₁)

=(2-1)/(4-(-1)

=1/5

Equation of AB bar is:

y-y₁= m(x-x₁)

y-1 = 1/5(x-(-1)

y-1= 1/5x+1/5

y= (x/5)+(1/5)+1

y= (x+1+5)/5

y=(x+6)/5

y=(x/5)+(6/5)

Therefore, slope =1/5, y-intercept = 6/5.

Give the slope and y-intercept (-6, -3) and (2, 6).

Let A=(-6,-3), B=(2,6)

Slope=(y₂- y₁)/(x₂ - x₁)

=(6-(-3))/2-(-6)

=9/8

Equation of AB bar is:

y-y₁ = m(x-x₁)

y-(-3) = (9/8)[x-(-6)]

y+3 = (9/8)(x+6)

y = (9/8)x + 54/8 -3

y = (9x+54-24)/8

y = (9x+30)/8

y= (9x/8)+(30/8)

y=(9x/8)+(15/4)

Therefore, slope = 9/8, y-intercept = 15/4.