Question

A line includes the points (0, –16) and (18, –15). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

`y=(1)/(18)x-16`

Explanation:

`\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=(y_2-y_1)/(x_2-x_1)$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}`

Given points:

• Let (x₁, y₁) = (0, -16)
• Let (x₂, y₂) = (18, -15)

Substitute the given points into the slope formula to find the slope of the line:

`\implies \textsf{Slope}\;(m)=(-15-(-16))/(18-0)=(1)/(18)`

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

The y-intercept is the value of y when x = 0.

Therefore, from the given point (0, -16), the y-intercept of the line is -16.

Finally, substitute the found slope and y-intercept into the formula:

`\implies y=(1)/(18)x-16`