Question

For each part, write the equation that represents the line in slope-intercept form (y = mx + b) and standard form (ax + by = c where a, b, and c are integers and a is not negative).

Answer 1

Graph

`y = -x+1` --- Slope intercept form

`y +x= 1` --- Standard form

Points

`y = 2x-2` --- Slope intercept form

`y -2x=-2` --- Standard form

Explanation:

Solving (a): The graph.

From the graph, we have:

`(x_1,y_1) = (1,0)`

`(x_2,y_2) = (0,1)`

First, calculate the slope

`m = (y_2 - y_1)/(x_2 - x_1)`

This gives:

`m = (1 - 0)/(0 - 1)`

`m = (1 )/(- 1)`

`m = -1`

The slope intercept equation is:

`y = m(x-x_1)+y_1`

So, we have:

`y = -1(x-1)+0`

`y = -1(x-1)`

`y = -x+1`

In standard form:

`y = -x+1`

Add x to both sides

`y +x= x-x+1`

`y +x= 1`

Solving (b): The points

From the graph, we have:

`(x_1,y_1) = (0,-2)`

`(x_2,y_2) = (3,4)`

First, calculate the slope

`m = (y_2 - y_1)/(x_2 - x_1)`

This gives:

`m = (4 - (-2))/(3 - 0)`

`m = (6)/(3)`

`m=2`

The slope intercept equation is:

`y = m(x-x_1)+y_1`

So, we have:

`y = 2(x-0)-2`

`y = 2(x)-2`

`y = 2x-2`

In standard form:

`y = 2x-2`

Subtract 2x from both sides

`y -2x= 2x-2x-2`

`y -2x=-2`