How do you write equation of the line in slope-intercept form given the y-intercept and another point?

Question

(2,2), (0,5)

Answer 1

Do you remember how to find the slope given two points? Slope (m)= change in y/change in x (change-- which is also referred to as delta, or a tiny triangle).

x y
(2 2)
(0 5)

M= Y2 - Y1 / X2 - X1
M=5-2/0-2= 3 / -2 right?
so therefore, the slope is (-3/2).
Now you must remember the general equation of a line:
y-y1=m(x-x1)

The variables y and x without a number after it you keep the same. So, picking point (2,2) to work with and plug in:
y-2= -3/2(x-2) and simplify to [[[[[[ y= -3/2x + 5 ]]]]]]]].

You could also try to use point (0,5) which if plugged in would look like this: y-5= -3/2(x-0). Simplified, it would look like... y= -3/2x + 5. So either point works.

Answer 2

Recognize that delY/delX = m = slope; where delY = y1 - y0 and delX = x1 - x0 which are just the ranges in the Y and X directions. Point 0 = (x0,y0) = (0,5) and point 1 = (x1,y1) = (2,2) which are the given points. Thus, your slope is delY/delX = (2 - 5)/(2 - 0) = -3/2 = m

The general equation for a straight line is y = mx + b; where b is the intercept. Thus, we have y = -3/2x + b and b = y when x = 0. Good news, we have that in point 0 where when x = 0, y = 5 = b. So y = -(3/2)x + 5 is the specific equation for the line running through the two given points.

Had we not been able to do this by inspection (noting the point 1 lies on the x = 0 point), we could solve for b by doing delY/delX = m = -3/2 = (y - y0)/(x - x0); so that, (-3/2)(x - x0) = (-3/2)(x - 0) = y - y0 = y - 5. Then combining terms and stuff, we get (-3/2)x = y - 5 and y = (-3/2)x + 5, which, thank goodness, is the same as we got by inspection.

Answer 3

First, you're able to desire to sparkling up it for y. 2x-3y=12 2x=12+3y 2x-12=3y 2/3x-4=y Then, for the perpendicular line, you're taking the adverse reciprocal of the slope, -3/2. that's the slope of the perpendicular line. you are able to then use the equation y-y1=m(x-x1). replace interior the extensive-unfold values, you get y-6=-3/2(x-2). in case you prefer to sparkling up that each physique out, you get y=-3/2x+9, yet that's often pointless.

Answer 4

slope ischange in Y divided by change in X

so your slope is (5-2)/(2-0) or 3/2.

Y = 3/2x+5

Answer 5

you use the slope formula which is y2-y1 over x2-x1 to find your slope, then you put it in point slope form which is y-y1=m(x-x1). then you solve for y and you should get something in y=mx+b form