Answer:
y=3/2x + 18
Step-by-step explanation:
So when two lines are perpendicular, that simple means the slope are reciprocals, and the signs are opposite. So for example if one equation had a slope of [tex]\frac{a}{b}[/tex], the equation that is perpendicular, would have a slope of [tex]-\frac{b}{a}[/tex]. So the first step would be to find the slope of 2x+3y=4. To find the slope we can convert it into slope-intercept form which is y=mx+b where m is the slope, and this is done by isolating y, as you can see the y is alone in the slope-intercept form.
Original equation:
2x + 3y = 4
subtract 2x from both equations:
3y = -2x + 4
Divide both sides by 3
y = -2/3x + 4/3
The y-intercept doesn't really matter in this case, what really matters is the slope, and the slope is the coefficient of x, since as x increases by 1, it will increase by the amount of the coefficient, because the slope is rise/run and since the run is 1, if you increase x by 1, the run is the slope, which is the coefficient. The slope in this case is -2/3. So the reciprocal of the slope is 3/2 (notice how the sign is the opposite as well). Now we have the equation
y=3/2x + b
To find the y-intercept, you simply use the point that was given (-2, 15). Plug in -2 as x, and 15 as y to find the value of b
Original equation
y=3/2x + b
Plug in known values:
15 = 3/2(-2) + b
Multiply the fraction:
15 = -6/2 + b
Simplify the fraction:
15 = -3 + b
Add 3 to both sides
18 = b
This gives you the equation
y=3/2x + 18
