Question

Write an equation in slope-intercept form for the line that satisfies the following condition.

passes through (10, 3), perpendicłlar to the graph of y = 4x+16

Answer 1

The equation of the line we want to write is 4y = -x + 22

Explanation:

Here, we want to write the equation of a line

.

The standard equation of a straight line is given as:

y = mx + c

where m is the slope and c represents the y-intercept

Now, let’s look at the line y = 4x + 16

The slope of this line is 4

Now, the equation of the line we want to write is perpendicular to this line

When two lines are perpendicular, the product of their slopes = -1

Hence;

m * 4 = -1

m = -1/4

So the slope of the line we want to write is -1/4

Now, using the point-slope form for the new equation;

y-y1/x-x1 = m

From the point given (x1,y1) = (10,3)

Thus;

y-3/x-10 = -1/4

4(y-3) = -1(x - 10)

4y - 12 = -x + 10

4y = - x + 10 + 12

4y = -x + 22