Given:
It is given that the slope [tex]m=-\frac{3}{4}[/tex] and contains the point (2,3)
We need to determine the graph of the line.
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the point (2,3) and the slope [tex]m=-\frac{3}{4}[/tex] in the above formula, we get;
[tex]y-3=-\frac{3}{4}(x-2)[/tex]
[tex]y-3=-\frac{3}{4}x+\frac{3}{2}[/tex]
[tex]y=-\frac{3}{4}x+\frac{9}{2}[/tex]
Thus, the equation of the line is [tex]y=-\frac{3}{4}x+\frac{9}{2}[/tex]
Graphing the line:
The equation of the line can be graphed by plotting the x and y intercepts.
The x - intercept is the value of x when y = 0. Thus, we get;
[tex]0=-\frac{3}{4}x+\frac{9}{2}[/tex]
[tex]-\frac{9}{2}=-\frac{3}{4}x[/tex]
[tex]6=x[/tex]
Thus, the x - intercept is (6,0)
The y - intercept is the value of y when x = 0. Thus, we get;
[tex]y=-\frac{3}{4}(0)+\frac{9}{2}[/tex]
[tex]y=\frac{9}{2}[/tex]
[tex]y=4.5[/tex]
Thus, the y - intercept is (0,4.5)
Hence, plotting these points and joining the line, we get the graph of the line [tex]y=-\frac{3}{4}x+\frac{9}{2}[/tex]
