Question

18. Write the slope-intercept form of the line described in the following:Perpendicular to y = 3x + 1 and passing through (-3, 5)

Answer 1

y = (-1/3)x + 4

Step-by-step explanation:

The slope-intercept form of a line can be calculated as:

`y=m(x_{}-x_1)+y_1_{}`

Where (x1, y1) is a point in the line and m is the slope.

On the other hand, two lines are perpendicular if the product of their slopes is equal to -1. It means that the slope of a line that is perpendicular to y = 3x + 1 can be calculated as:

`\begin{gathered} 3\cdot m=-1 \\ (3\cdot m)/(3)=-(1)/(3) \\ m=-(1)/(3) \end{gathered}`

Because the slope of the line y = 3x + 1 is 3.

Then, replacing m by -1/3 and (x1, y1) by (-3, 5), we get that equation of the line is:

`\begin{gathered} y=-(1)/(3)(x-(-3))+5 \\ y=-(1)/(3)(x+3)+5 \end{gathered}`

Finally, applying the distributive property, we get:

`\begin{gathered} y=-(1)/(3)x-(1)/(3)\cdot3+5 \\ y=-(1)/(3)x-1+5 \\ y=-(1)/(3)x+4 \end{gathered}`

Therefore, the slope-intercept form of the line is: y = (-1/3)x + 4