SOLUTION: Write an equation in slope-intercept form of a line with the following characteristics. Perpendicular to the graph of: y=3/2x-3 with a y-intercept of 5.

Question 175879This question is from textbook
: Write an equation in slope-intercept form of a line with the following characteristics. Perpendicular to the graph of: y=3/2x-3 with a y-intercept of 5. This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: a y-intercept of 5 means that the point (0,5) is on the graph.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point

.

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 5 to both sides.

Combine like terms.

So the equation of the line perpendicular to that goes through the point

is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the perpendicular line (green) through the point

.

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