Question

You are to demonstrate that you understand slope. You are to draw two graphs of lines. One line needs to have a slope of 2/3 and the second line needs to have a slope of -4.

Answer 1

In mathematics, the slope is used to describe the steepness and direction of straight lines.

Then knowing the slope and one point in the line , you can write the equation of this line.

If m is the slope of the line

The equation of this line is Y = mX + d  

d indicates the intersection point of the line with the y-axis, where X=0 (0,d)

To draw a line in the coordinate system (x,y), we have to calculate two points and then draw a line that passes through those two points. The first point is the intersection of the line with the vertical y-axis. We already know that it is (0,d) and another point can be the intersection of the line with the horizontal x-axis. To find it we have to substitute in the equation making Y = 0.

First equation : Y = 2/3X + b  where b is any value where the line will cut to the y-axis

intersection point of this line with the vertical y-axis => (0,b)

intersection point of this line with the horizontal x-axis, making Y=0

2X/3 + b = 0

X = -3b/2

intersection point of the line with the horizontal x-axis => (-3b/2,0)

Second equation : Y = -4X + c where c is any value where this line will cut to the y-axis

intersection point of the line with the vertical y-axis => (0,c)

intersection point of this line with the horizontal x-axis, making Y=0  

-4X + c = 0

X = -c/-4 = c/4

intersection point of the line with the horizontal x-axis => (c/4,0)

$\textit{\textbf{Spymore}}$​​​​​​