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 [tex]y = \frac{1}{5}x + 6[/tex]
Solution:
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 = [tex]\frac{1}{5}[/tex]
Now substitute m = [tex]\frac{1}{5}[/tex] and c = 6 in slope intercept form
[tex]y = \frac{1}{5}x + 6[/tex]
Thus the required equation of line is found
