Question

Your Turn!Write the equation of a line (in slope-intercept and point-slopeform) with a slope of 2 that passes through the point (5, -3).

Answer 1

The equation of a line can be represented in many forms. We are to express the equation in slope intercept form.

The general formula used for the slop-intercept formulation is as follows:

`y\text{ = m}\cdot x\text{ + c}`

Where,

`\begin{gathered} y\colon\text{ The vertical coordinate position} \\ m\colon\text{ The slope of the equation ( constant )} \\ x\colon\text{ The horizontal coordinate position} \\ c\colon\text{ The y-intercept ( constant )} \end{gathered}`

The equation of a line allow us to determine the coordinates of any point on the line by stating its coordinates in the form, in the cartesian coordinate system:

`(\text{ x, y )}`

From the general slop-intercept formulation expressed initially we see that we have two constants ( m & c ). These constants are determined using points that lie on the line. These very same constants also makes an equation of a line unique from all the other equations.

From the data given, The slope of the line is 2. We will go ahead and assign the value to the constant m as follows:

`m\text{ = 2}`

Then we plug in the value of intercept in the initial general slop-intercept form as follows:

`y\text{ = 2}\cdot x\text{ + c}`

Now to evaluate the constant ( c ) we need a pair of coordinates that must lie on the line for which the equation is derived. The data provides us with this point as:

`(\text{ 5 , -3 )}`

We will go ahead and plug in the respective coordinates in the slope-intercept form derived above:

`\begin{gathered} x\text{ = 5 , y = -3} \\ -3\text{ = 2}\cdot(5)\text{ + c} \\ -3\text{ = 10 + c} \\ c\text{ = -13} \end{gathered}`

We have determined the two constants ( m & c ). Now to express the unique equal