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

Jun 24, 2018

Slope (gradient) $= 5$

y-intercept $= 13$

#### Explanation:

Given: $\left(y - 3\right) = 5 \left(x + 2\right)$

$\textcolor{b l u e}{\text{Answering the question}}$

Write as $y - 3 = 5 \left(x + 2\right)$

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)

$y = 5 x + 13$

Compare to the standardised form $y = m x + c$

Where the slope (gradient) $m = 5$

Where $c = 13$

The y-intercept $= c = 13$

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$\textcolor{b l u e}{\text{Foot note}}$

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

Substitute $0 \text{ for } x$ and we have:

$y = 5 \left(0\right) + 13$

$y = 0 + 13$