Question

Find the slope of each line and then write it's equationQuestion a)

Answer 1

slope: -3/2

equation of the line: y = (-3/2)x

Explanation

The slope, m, of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:

`m=(y_2-y_1)/(x_2-x_1)`

From the graph, this line passes through the points (0, 0) and (2, -3), then its slope is:

`\begin{gathered} m=(-3-0)/(2-0) \\ m=-(3)/(2) \end{gathered}`

Equation of a line in slope-intercept form

`y=mx+b`

where m is the slope and (0, b) is the y-intercept.

Given that the line intercepts the y-axis at the point (0, 0), then b = 0.

Substituting m = -3/2 and b = 0 into the general equation, the equation of this line is:

`\begin{gathered} y=-(3)/(2)x+0 \\ y=-(3)/(2)x \end{gathered}`