Write an equation in slope-intercept form for a line that is (a) parallel (b) perpendicular to the line y=-5x-3 and has a y-intercept if 6

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis

The given equation is y = - 5x-3

Compared to y = mx + c, the slope, m is - 5

a) if two lines are parallel, it means that they have equal slope. Therefore the slope of the line parallel to y = - 5x-3 is - 5. Since the y intercept is 6, the equation would be y = - 5x + 6

b) if two lines are perpendicular, the slope of one line is the negative reciprocal of the line perpendicular to it. Since the slope of the given line is - 5, the slope of the line perpendicular to it is 1/5. The equation becomes

y = x/5 + 6