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:

$y=5(0)+13$

$y=0+13$

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