Write an equation in slope-intercept form for the line that passes through (1, 1), and is perpendicular to the graph of 3x + 2y = -7

Answer 1

Remember when two line is perpendicular, the multiplicity of their slopes is -1

3x+2y=7

2y=7-3x

y=(-3x+7)/2

y=-3/2 x + 7/2

So the first slope is -3/2

The other line has slope k.

And k * (-3/2)= -1

So k=2/3

The formula of the line isL y=kx+b;

So;

y=2/3*x +b

Because the line passes through (1,1), we have x=1, y=1

substitute these number back to y=2/3*x+b

we have: 1=2/3 * 1 +b

so b= 1-2/3=1/3

Therefore, the line: y=2/3x +1/3

Answer 2

The slopes of perpendicular lines are negative reciprocals (flip and negate). So first, we need to find the slope of the given line to determine the slope of the perpendicular line.

3x + 2y = -7

1. rewrite the line in slope-intercept form (y=mx +b). Subtract 3x from both sides: 2y = -3x -7. Then divide everything by 2 to get y by itself: y = (-3/2)x -(7/2).
2. identify the slope (m) of the given line. The slope is the coefficient in front of the x. The slope of the given line is -3/2. That means that the slope of the perpendicular line will be the negative reciprocal (flip and negate) which is 2/3.
3. Use the perpendicular slope, 2/3, and the given point to write the equation of the perpendicular line.
4. There are two methods for this. The first is using slope-intercept form directly. Plug in the x-value from the point (1), the y-value from the point (1) and the m (2/3), and solve for the y-intercept, b: y=mx+b => 1= (2/3)(1) +b => 1= (2/3)+b. So b= 1- (2/3) which simplifies to 1/3.
5. Rewrite the equation with the slope and y-intercept: y = (2/3)x + (1/3)

The other method to write the equation is to plug the point and slope into point-slope form and simplify into slope-intercept form. Point-slope form is (y-y₁)=m(x-x₁). For this problem, x₁=1, y₁=1, and m= (2/3). Plug in: (y-1)= (2/3)(x-1).

Distribute 2/3: y-1= (2/3)x - 2/3.

Add 1 to both sides: y = (2/3)x + 1/3.