Question

Write the equation of a line in slope intercept form that passes through the point(-6, 7) and is parallel to the line represented by 5x + 2y = 10. 

Answer 1

The equation of a line in Slope-Interecept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

Given the following equation:

`5x+2y=10`

You need to solve for "y" in order to write it in Slope-Intercept form:

`\begin{gathered} 2y=-5x+10 \\ y=(-5x)/(2)+(10)/(2) \\ \\ y=-2.5x+5 \end{gathered}`

You can see that its slope is:

`m_1=-2.5`

Since the slopes of parallel lines are equal, you know that the slope of the other line is:

`m_2=-2.5`

Substitute the coordinates of the given point and the slope into this equation:

`y=mx+b`

And solve for "b". This is:

`\begin{gathered} 7=-2.5(-6)+b \\ 7=15+b \\ 7-15=b \\ b=-8 \end{gathered}`

Finally, knowing the slope and the y-intercept, you can determine that the equation of this line in Slope-Intercept form, is:

`y=-2.5x-8`