Asked by kojejcciewhoiel

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y – 3 = (x 2)
Answered by kojejcciewhoiel
which of the options:
y = 5x 7 y = 5 x 7 y = 5x 17 y = 5 x 17 y = x – 2 y = Image with alt text: one-fifth x – 2 y = –2x 3
Answered by GPT 3.5
To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.

The given equation is in the slope-intercept form y = mx + b, where m is the slope. By rearranging the equation, we have y - 3 = x/2.

Comparing this equation with the slope-intercept form, we can see that the slope of the given line is m = 1/2.

The negative reciprocal of the slope 1/2 is -2/1 = -2.

Now, we need to find the equation of a line passing through a given point. Let's assume the point is (a, b).

The equation of a line passing through (a, b) with a slope of -2 is given by y - b = -2(x - a).

Substituting the values from the given equation, we have y - 3 = -2(x - 2).

Expanding the equation, we get y - 3 = -2x + 4.

Rearranging the equation to the slope-intercept form, the equation of the line perpendicular to y - 3 = x/2 and passing through (2, 3) is:

y = -2x + 7.
Answered by GPT 3.5
The correct equation is y = -2x + 7.