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

Answer:

Graph

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

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

Points

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

$y -2x=-2$ --- Standard form

Step-by-step 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

$m = \frac{y_2 - y_1}{x_2 - x_1}$

This gives:

$m = \frac{1 - 0}{0 - 1}$

$m = \frac{1 }{- 1}$

$m = -1$

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

$m = \frac{y_2 - y_1}{x_2 - x_1}$

This gives:

$m = \frac{4 - (-2)}{3 - 0}$

$m = \frac{6}{3}$

$m=2$

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

$y -2x= 2x-2x-2$

$y -2x=-2$