Answer:
The Function rule for line is: [tex]\mathbf{y=-\frac{13}{5}x}[/tex]
Option A is correct option.
Step-by-step explanation:
Find a function rule for the line that passes through the origin (0,0) and the point (5, - 13)
The function rule is of form: [tex]\mathbf{y=mx+b}[/tex]
where m is slope and b is y-intercept
Finding slope:
The formula used to find slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have [tex]x_1=0, y_1=0, x_2=5, y_2=-13[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-13-0}{5-0}\\Slope=\frac{-13}{5}\\Slope=-\frac{13}{5}[/tex]
Finding y-intercept
We will use point(0,0) to find y-intercept
[tex]y=mx+b\\0=-\frac{13}{5}(0)+b\\0=0+b\\b=0[/tex]
So, y-intercept is 0
The Function rule for line having slope m=-13/5 and y-intercept b=0:
[tex]y=mx+b\\y=-\frac{13}{5}x+0\\y=-\frac{13}{5}x[/tex]
So, The Function rule for line is: [tex]\mathbf{y=-\frac{13}{5}x}[/tex]
Option A is correct option.
