Answer :
Answer:
Check the explanation.
Step-by-step explanation:
As the graph of a linear function f passes through the point (-2,-10) and has a slope of 5/2.
As the slop-intercept form is given by:
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept.
substituting the values (-2, -10) and m = 5/2 in the slop-intercept form to determine y-intercept.
[tex]y = mx+b[/tex]
[tex]-10=\frac{5}{2}\left(-2\right)+b[/tex]
[tex]-\frac{5}{2}\cdot \:2+b=-10[/tex]
[tex]-5+b=-10[/tex]
[tex]-5+b+5=-10+5[/tex]
[tex]b=-5[/tex]
And the equation of the line in the slope-intercept form will be:
[tex]y = mx+b[/tex]
putting b = -5 and slope = m = 5/2
[tex]y = mx+b[/tex]
[tex]y=\frac{5}{2}x+\left(-5\right)[/tex]
[tex]y=\frac{5}{2}x-5[/tex]
Determining the zero of function.
As we know that the real zero of a function is the x‐intercept(s) of the graph of the function.
so let us determine the value of x (zero of function) by setting y = 0.
[tex]0=\frac{5}{2}x-5[/tex]
[tex]\frac{5}{2}x-5=0[/tex]
[tex]\frac{5}{2}x=5[/tex]
[tex]5x=10[/tex]
[tex]x=2[/tex]
Therefore, the zeros of the function will be:
- x = 2