Question

Write and equation in slope intercept form through (5,2) and parallel to the given line y=-5x+3

Answer 1

For Parallelism condition, the slope of the two(2) lines are equal.

i.e:

`m_1=m_2`

From the given equation of the line:

`y=-5x+3`

Comparing this with the standard straight line equation: y= mx + c, where m represents the slope, we have:

`m=-5`

Since the lines are parallel; the new slope is also equal to -5.

Thus,

`\begin{gathered} m_1=m_2 \\ m_2=-5 \end{gathered}`

Now that we know the slope and a point (5, -2), we can use the slope formula:

`\begin{gathered} m=(y-y_1)/(x-x_1) \\ m=-5 \\ \text{from the point (5,2);} \\ x_1=5,y_1=2 \end{gathered}`

Thus, we have:

`\begin{gathered} -5=(y-2)/(x-5) \\ \text{cross}-\text{multiply;} \\ y-2=-5(x-5) \\ y-2=-5x+25 \\ y=-5x+25+2 \\ y=-5x+27 \end{gathered}`

Hence, the equation in slope-intercept form is:

`y=-5x+27`