Find the equation of the line with y intercept 2 and perpendicular to the line y = 2/3x -4
so it would not be a -b? so it would be 3/2x + 2?
2 = -3/2(0) + b
2 = b
y = mx + b
y = -3/2x + 2
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 slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
The given line is y = (2/3)x - 4. We can compare this equation to the slope-intercept form and see that the slope (m) is 2/3.
The negative reciprocal of 2/3 is found by flipping the fraction and changing the sign, resulting in -3/2. This will be the slope of the perpendicular line.
Since we are given that the y-intercept is 2, we can plug in the values into the slope-intercept form to find the equation of the line:
y = (-3/2)x + 2
Thus, the equation of the line that is perpendicular to y = (2/3)x - 4 and has a y-intercept of 2 is y = (-3/2)x + 2.
so you want the equation of the line
y=-3/2 x + b
intercept is when x is zero, so b=2