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Answer 1 · 2018-01-18T01:53:58

#y=5x-2#

We know that the linear equation is in the form of

#y=mx+b#, #m# is the slope#, #b# is the y-intercept

Given: #m=5#, passes through #(3,13)#

#:.y=5x+b#

We also know that it passes through #(3,13)#, so we can plug that in for #x=3, y=13#

#13=5*3+b#

#13=15+b#

#b=-2#

#:. y = 5x-2#

Answer 2 · 2018-01-18T01:59:20

In point-slope form: #y-13=5(x-3)#

In #y=mx+b# form: #y=5x-2#

We can use the point-slope formula to find the equation of the line

#y-y_1=m(x-x_1)#

Where #m# is the slope and #(x_1,y_1)# is a point on the line

Given: #m=5# and #(x_1,y_1)->(3,13)#

#y-13=5(x-3)#

This is the equation in point-slope form but this can be rewritten in #y=mx+b# form

To do that, we'll solve the above equation for #y#

#y-13=5x-15#

#y-13color(red)(+13)=5x-15color(red)(+13)#

#y-0=5x-2#

#y=5x-2#

The graph of the line is shown below:

graph{5x-2 [-10, 10, -5, 5]}