Question

Write the slope-intercept form of the equation that fits the conditions.

Perpendicular to y=-1/3x+1

Passes through (5,-2)

How do I solve this??

Answer 1

y = 3x - 17

Explanation:

Here is the point-slope form of the equation of a line.

`y - y_1 = m(x - x_1)`

If you are given a slope, m, and a point on the line, (x1, y1), you just plug in the values into the equation above, and you get the equation of the line.

In your problem, you are given a point on the line, (5, -2). Now you need the slope of the line. Your line is perpendicular to the given line. The slopes of perpendicular lines are negative reciprocals. If you know the slope of a line, the slope of its perpendicular is found by flipping the fraction and changing the sign.

The given line has slope -1/3.

Flip -1/3 to get -3.

Now change the sign to get 3.

The slope of the line you need is 3. The line passes through point (5, -2).

Now we use the point-slope equation and we plug in the values we have.

`y - y_1 = m(x - x_1)`

`y - (-2) = 3(x - 5)`

`y + 2 = 3x - 15`

`y = 3x - 17`