write an equation that satisifies the given conditions: perpendicular to y=-3x+7 through (3,5)

In this case, the slope of the given line is m=-3. The slope of the perpendicular line is m1 such that m.m1=-1.

Therefore m1=-1/(-3)=1/3
If it has to pass through a point (x1,y1), the equation of the line is then
y=m1(x-x1)+y1

Can you continue from here?

The equation for a straight line is y = mx + b where m is the slope. Therefore, the slope of this line is -3. The line perpendicular to this line has a slope of the negative reciprocal or 1/3.

y = (1/3)x + 7 or
3y = x + 21
Now substitute either value for x or y and solve for the other; for example, substitute 5 for y and solve for x, then write it in standard form.

To write an equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope to obtain the slope of the new line.

First, let's identify the slope of the given line, y = -3x + 7. In this equation, the coefficient in front of x is -3. Therefore, the slope of the given line is -3.

To obtain the slope of the perpendicular line, we take the negative reciprocal of -3. The negative reciprocal is found by flipping the fraction and changing the sign, so the negative reciprocal of -3 is 1/3.

Now, let's use the point-slope form of the equation of a line to write the equation. The point-slope form is given by:

y - y1 = m(x - x1),

where (x1, y1) represents a point on the line, and m is the slope.

We are given a point (3, 5) that lies on the perpendicular line. Substituting the values into the equation, we get:

y - 5 = (1/3)(x - 3).

Simplifying this equation gives us the final answer:

y - 5 = (1/3)x - 1.

This equation, y - 5 = (1/3)x - 1, satisfies the given conditions of being perpendicular to y = -3x + 7 and passing through the point (3, 5).