What is the slope and y-intercept of the line #(y - 3) = 5(x + 2)#?

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Answer 1 · 2018-06-24T09:20:46

Slope (gradient) #=5#

y-intercept #=13#

Given: #(y-3)=5(x+2)#

#color(blue)("Answering the question")#

Write as #y-3=5(x+2)#

Consider the right hand side

Multiply everything inside the brackets by 5

#y-3= 5 x+10#

Add 3 to both sides (gets rid of it on the left)

#y=5x+13#

Compare to the standardised form #y=mx+c#

Where the slope (gradient) #m=5 #

Where # c=13#

The y-intercept #=c=13#

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#color(blue)("Foot note")#

This is because the line crosses the y-axis at #x=0#

Substitute #0 " for "x# and we have:

#y=5(0)+13#

#y=0+13#