Question

"Write an equation in slope-intercept form for the trend line that is drawn." ​

Answer 1

`y=-3x`

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:

• (1, -3)
• (2, -6)

Substitute the two points into the slope formula to calculate the slope of the line:

`\implies m=(-6-(-3))/(2-1)=(-3)/(1)=-3`

`\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}`

Substitute the found slope and one of the points on the line into the point-slope formula:

`\implies y-(-3)=-3(x-1)`

`\implies y+3=-3x+3`

`\implies y=-3x`

Answer 2

• y = - 3x

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The line passes through the origin, therefore one point on the line is sufficient to determine the equation:

• y = kx, is the form of this equation

The point on the line is (1, - 3), so the line is:

• y = - 3x