write the equation of the line that is perpendicular to 4x-2y=10 and goes through the point (6,-9)

Answer 1

First, we need to rewrite the equation so that it is in slope-intercept form.

Slope-intercept form is defined as y = mx +b

where,

1. y = y-coordinate
2. m = slope
3. x = x-coordinate
4. b = y-intercept

So, for 4x - 2y = 10, we can use algebraic methods to rearrange the equation.

1. Subtract 4x from both sides.

-2y = 10 - 4x

2. Divide both sides by -2 to get y by itself.

y = 2x - 5 (note that because we divided by a negative number, our signs flipped)

3. Now that we have the equation in slope-intercept form, we need to find the equation for the line that is perpendicular to this line. A line that is perpendicular to another line will have a slope that is the opposite reciprocal of the original slope. An opposite reciprocal just means we flip the fraction and the sign.

The slope of the original line from step 2 is 2. Since 2 is the same thing as 2/1, we flip this fraction to 1/2 and then flip the sign from positive to negative to get the opposite reciprocal of -1/2.

This is the slope of the line that is perpendicular to our original line.

4. The last step is to utilize the given point and the slope of the line that is perpendicular to calculate the y-intercept, or b, for the line that is perpendicular to our original line.

point: (6, -9), where 6 is our x-coordinate and -9 is our y-coordinate

slope-intercept form with new slope: y = -1/2x + b

-9 = -1/2(6) + b

-9 = -3 + b

-6 = b

5. Now that we have our slope and y-intercept for the line that is perpendicular to our original line, we can use these values to write the equation of this line in slope-intercept form.

y = -1/2x - 6

This is the final answer.