m is the slope and m = 5.
c is the y - intercept and c = (0, -4).
What is slope and y - intercept?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
The equation of line T, shown in the graph can be written in the form
y = mx + c
where,
m is the slope and c is the y-intercept.
We have to find the value of m and c.
y - intercept is the point when it crosses the y - axis.
At that point x = 0.
So, from graph the y-intercept is (0, -4).
Now to find the slope.
From graph we have two points, (0, -4) and (1, 1).
So,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{1-(-4)}{1-0}= \frac{5}{1}=5[/tex]
Hence, the slope of the line T is 5.
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