When we are given a straight line drawn on the cartesian graph, i.e, having x and y coordinates, the gradient/slope is the change on the y-axis relative to change on the x-axis.
The x-axis is the horizontal axis and the y-axis is the vertical axis.
To get the gradient, we simply pick two points on the line and name them points 1 and 2. Thus, they will have the following attributes:
[tex]\begin{gathered} Point1=(x_1,y_1) \\ Point2=(x_2,y_2) \end{gathered}[/tex]
The gradient of a straight line is:
[tex]s=\frac{y_2-y_1}{x_2-x_1}[/tex]
So, in our question, we can pick our points 1 and 2 at
Point 1 = (-2, 6), (1,-3),
Point 2 = (0, 0), (2,-6)
Applying our formulae, we get:
[tex]\begin{gathered} s=\frac{0-6}{0-(-2)_{}}=-\frac{6}{2}=-3 \\ s=\frac{-6-(-3)}{2-1}=-\frac{3}{1}=-3 \\ \text{Any two points will give us a gradient of -3} \end{gathered}[/tex]
The gradient is -3.
As for the intercept on the y-axis, this is the point on the vertical axis where the graph cuts the graph. It can be visibly seen from our graph as occurring at y = 0.
However, it can be calculated via a formula to give us the form: y = mx + c.
where: m is the gradient/slope and c is the intercept on the y axis.
Formulae for getting conventional line equation is:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \frac{y-6}{x-(-2)}=-3 \\ -3x-6=y-6 \\ \text{Adding 6 to both sides gives:} \\ -3x=y \end{gathered}[/tex]
The line equation is therefore: y = -3x + 0
Slope = -3 AND
y-intercept = 0
