Question

What is the equation for the line in slope-intercept form?

Answer 1

Answer: y = 8x

Explanation:

The line passes through points (1,8) and (2,16).

Using this, we can first find the slope.

Slope = Δy/Δx = 8/1 = 8

So the slope is 8.

The equation is now

y = 8x + b

Let's use the point (1,8) to find the value of b now.

8 = 8 +b

b = 0

Therefore, y = 8x is the answer.

(you can skip the last step by noticing that the graph passes through the origin)

Answer 2

y = 8x

Explanation:

`\boxed{\begin{minipage}{8cm}\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}}`

From inspection of the given graph, two points on the line are:

• (0, 0)
• (2, 16)

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

`\implies m=(16-0)/(2-0)=(16)/(2)=8`

`\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 y-value of the point where the line crosses the y-axis. From inspection of the given graph, the y-intercept is zero. So b=0.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

`\implies y=8x+0`

`\implies y=8x`

Therefore, the equation for the line in slope-intercept form is:

• y = 8x