Answer:
A. In the graph,
Go 5 units left side from the origin in the x-axis then from that point go downward 6 unit, we will get (-5, -6),
Now, go 10 unit right from the origin in the x-axis then from that point go upward 3 unit, we will get (10, 3),
B. The slope of the line passes through (-5, -6) and (10, 3),
[tex]m=\frac{3-(-6)}{10-(-5)}=\frac{3+6}{10+5}=\frac{9}{15}=\frac{3}{5}[/tex]
C. Since, the equation of a line passes through [tex](x_1, y_1)[/tex] with slope m is,
[tex]y-y_1=m(x-x_1)[/tex]
Thus, the equation of the line is,
[tex]y+6=\frac{3}{5}(x+5)----(1)[/tex]
For y-intercept,
x = 0,
[tex]y+6 = \frac{3}{5}(0+5)\implies y = 3-6=-3[/tex]
That is, y-intercept is -3.
D. From equation (1),
[tex]5y + 30 = 3x + 15[/tex]
[tex]\implies 3x - 5y = 15[/tex]
Which is the required linear function.
