(Parallel and Perpendicular lines on a graph (math)

Question

Write an equation in​ slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. ​(negative 3​,7​); y equals one third x minus 1

Answer 1

The equation of the given line is in slope-intercept form:

y = (1/3)x - 1.

The slope of the given line is 1/3.

Every line perpendicular to that line has a slope that is the negative (opposite) reciprocal of 1/3.

So lines perpendicular to the given line have slope -3.

To write the equation of a line in the xy-plane it is necessary to know its slope and a point that is passes through (which we do), the point being (-3,7).

You have a choice how to determine the equation of that line.

Using point-slope:

y - y₁=m(x-x₁), where (x₁,y₁) is the given point and m is the slope:

y - 7 = -3(x - (-3))

y - 7 = -3(x+3), now isolate y to place in slope-intercept form:

y - 7 = -3x -9

y = -3x - 2

Using slope-intercept

y = mx + b (where b is unknown)

7 = -3(-3) + b

7 = 9 + b

b = -2

y = -3x - 2

Visit the following Desmos graph to see the results of the above. Use the slider on k to see other lines perpendicular to the given line.

desmos.com/calculator/uzvhx80hoy

Select the URL above, right-click, choose "Go to..." from drop-down menu.