Question

What is an equation of the line perpendicular to the one shown that passes through (-3,-4)?

Answer 1

D.
`y = (2)/(3)x - 2`

Explanation:

To find the equation of the line that is perpendicular to the one shown on the graph, which passes through (-3, -4) we need to find the slope of the line, m, and the y-intercept, b.

The equation would be in the slope-intercept form given as y = mx + b.

The slope of the line would be the negative reciprocal of the slope of the line shown on the graph.

So, first, find the slope of the line shown in the graph using the points on the line, (0, 3) and (4, -3):

`m = (y_2 - y_1)/(x_2 - x_1) = (-3 - 3)/(4 - 0) = (-6)/(4) = -(3)/(2)`

Since the slope of the line shown on the graph is -³/2, therefore the slope of the line that is perpendicular to the line shown would be the negative reciprocal of -³/2. Negative reciprocal of -³/2 is ⅔.

Therefore, the slope, m, of the line that is perpendicular to the line shown is ⅔.

Let's find its y-intercept using the point given, (-3, -4) that the line passes through and its slope, m = ⅔.

Substitute m = ⅔, x = -3 and y = -4 in y = mx + b, to find b.

-4 = ⅔(-3) + b

-4 = -2 + b

Add 2 to both side

-4 + 2 = b

-2 = b

b = -2

Substitute m = ⅔, and b = -2 in y = mx + b.

The equation of the line would be:

`y = (2)/(3)x +(-2)`

`y = (2)/(3)x - 2`