Answer:
1) Option B [tex]y=-\frac{4}{5}x +7[/tex]
2) Option A [tex]y-0=\frac{1}{3} (x+6)[/tex]
Step-by-step explanation:
Question 1:
We will find the slope of the line with the help of the given points (0, 7) and (5, 3)
.
[tex]Slope_1 = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope_1 = \frac{3-7}{5-0} =-\frac{4}{5}[/tex]
Now, we will use any one of the given points and substitute its x and y coordinates in the standard form of equation of a line to find the y-intercept:
[tex]y=mx+c[/tex]
[tex]7=-\frac{4}{5}(0)+c[/tex]
[tex]7=c[/tex]
Therefore, the equation of the line 1 is [tex]y=-\frac{4}{5} x+7[/tex]
Question 2:
We are given the slope of this line and a point (-6, 0) which the line passes through.
[tex]Slope_2=\frac{1}{3}[/tex]
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-0=\frac{1}{3}(x-(-6))[/tex]
[tex]y-0=\frac{1}{3} (x+6)[/tex]
Therefore, the equation of line 2 is [tex]y-0=\frac{1}{3} (x+6)[/tex].
