Answer:
[tex]y=-\frac{5}{7}x+5[/tex]
Step-by-step explanation:
The equation of a line can be written in the form of y= mx +c, where m is the slope and c is the y-intercept. This is also known as the slope-intercept form.
Identify the value of the slope, m:
Given that the slope is [tex]-\frac{5}{7}[/tex], m= [tex]-\frac{5}{7}[/tex].
Substituting the value of m into the equation:
[tex]y=-\frac{5}{7} x+c[/tex]
Identify the value of the y-intercept:
Given that the y-intercept is 5, c= 5.
Substitute c= 5:
[tex]\bf{y=-\frac{5}{7}x+5}[/tex]
Thus, the equation of the line is [tex]\bf{y=-\frac{5}{7} x+5}[/tex].
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