Determine an equation of a line in slope-intercept form that goes through a given point and is parallel or perpendicular to a given line

Question

Determine an equation of a line that passess through the point (8,6) and is perpendicular  to the graph of y=-7/3x+8/3

Answer 1

 Let's start with a review of the slope-intercept form: y = mx + b
m stands for the slope
b stands for the y-intercept, which is the point where the line crosses the y-axis.

Now for the slope! You're being asked to give the slope of a line that is perpendicular to another,
in this case y = -7/3x + 8/3. From slope-intercept form, we know that the slope of the first line is -7/3. To find the slope of a line perpendicular to the first, all you have to do is take the opposite reciprocal, which is a fancy way of saying- flip the sign and reverse the fraction. So, the slope of your perpendicular line is going to be 3/7 (turn the negative into a positive, and flip numerator/denominator).

Now that we know the slope, we can use the given point to write an equation! To do that, we need to use point-slope form:
y - y_{1 =} m(x - x_x)

We know that m = 3/7, y₁= 6, and x₁= 8 (Because the new line has to pass through (8,6))
y- 6 = (3/7)(x - 8)
y - 6= 3/7x - 24/7

y = 3/7x + 18/7