Here is another riddle: The sum of two numbers is less than 2. If we subtract the second number from the first, the difference is greater than 1. What are the two numbers? The riddle can be represented by a system of inequalities. Write an inequality for each statement. These graphs represent the inequalities in the system. Which graph represents which inequality?

a) Equation in slope-intercept form for a line that is parallel to  the line y = -5x - 3 and has a y-intercept of 6 is y = -5x + 6

b) Equation in slope-intercept form for a line that is perpendicular to  the line y = -5x - 3 and has a y-intercept of 6 is

We have to find the equation in slope intercept form

The slope intercept form is given as:

y = mx + c

where "m" is the slope of line and "c" is the y -intercept

a) Equation in slope-intercept form for a line that is parallel to  the line y = -5x - 3 and has a y-intercept of 6

Given line has equation y = -5x - 3

On comparing given equation y = -5x - 3 with slope intercept form, we get

slope of line "m" = -5

We know that slopes of parallel lines are equal

so slope of line parallel to given line is also -5

Now substitute m = -5 and c = 6 in slope intercept form

y = -5x + 6 is the required equation

b) Equation in slope-intercept form for a line that is perpendicular to  the line y = -5x - 3 and has a y-intercept of 6

We already found that slope of line with equation y = -5x - 3 is -5

We know product of slopes of perpendicular lines are equal to -1

-5 x slope of line perpendicular to given line = -1

slope of line perpendicular to given line =

Now substitute m = and c = 6 in slope intercept form

Thus the required equation of line is found