Write the equation of the line in slope-intercept and standard form whose graph passes through the given point and has the given slope:
(3,-2), m = -3/2
THANK YOU :)
you know it must look like:
y = mx + b
given: m = -3/2, so
y = (-3/2)x + b
but (3,-2) lies on it, so
-2 = (-3/2)(3) + b
-2 + 9/2 = b
b = 5/2
y = (-3/2)x + 5/2
or, just start with what you are given: a point and a slope. Ding ding - use the point-slope form of the line:
y+2 = -3/2 (x-3)
now just rearrange stuff, and you will get Reiny's equation.
To find the equation of a line in slope-intercept form (y = mx + b), you need to substitute the values of the point and the slope into the equation and solve for the y-intercept (b). Let's do that:
Given the point (3, -2) and the slope (m = -3/2), we can substitute these values into the slope-intercept form equation (y = mx + b):
-2 = (-3/2)(3) + b
Next, simplify the equation by multiplying the slope (-3/2) by 3:
-2 = (-9/2) + b
To isolate b, add 9/2 to both sides of the equation:
-2 + 9/2 = b
To get a common denominator, multiply -2 by 2/2:
-4/2 + 9/2 = b
Combine the fractions:
5/2 = b
Now that you have the value of the y-intercept (b = 5/2), you can write the equation in slope-intercept form:
y = (-3/2)x + 5/2
To convert the equation to standard form (Ax + By = C), you need to eliminate any fractions. Multiply the entire equation by 2 to get rid of the denominators:
2y = -3x + 5
Next, move the variables to one side and the constant to the other side of the equation:
3x + 2y = 5
Therefore, the equation of the line in slope-intercept form is y = (-3/2)x + 5/2, and the equation in standard form is 3x + 2y = 5.