what is an equation for the line that passes through the coordinates (2,0) and (0,3)?
(1) y=-3/2x+3
(2) y=-3/2x-3
(3) y=-2/3x+2
(4) y=-2/3x-2
explain the steps too please. :)
In-order to get the equation of a line you need 2 points. This fact will remain true for the rest of your life (when you get to higher levels of math) all you need is 2 points.
A point is usually referred to as X1, Y1.
The slope of a line is (Y2-Y1)/(X2-X1)
STEP #1: Insert points into slope equation.
Point 1: X1,Y1 = (2,0)
Point 2: X2,Y2 = (0,3)
Slope = 3-0 / 0-2 = 3/2
STEP #2: Once you have the slope, solve for B in the equation of a line [y=ax + b where a = the slope and b = y-intercept]
..
Y = ax + b
we know the slope is 3/2
so
Y = 3/2x + b
we know 2 points, so you can plug any of them in to solve for b
Let's use 2,0
0 = 3/2 (2) + b
0 = 3 + b
b= -3
Solution: Y= AX + B ..
Y = 3/2X -3
(2)
good luck..
thanks. :)
To find the equation of the line that passes through the coordinates (2,0) and (0,3), we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
Where m is the slope of the line and b is the y-intercept.
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (2,0) and (0,3):
m = (0 - 3) / (2 - 0)
m = -3 / 2
Step 2: Substitute the values of the slope (m) and one of the given points (x1, y1) into the equation:
We'll use (2,0) as (x1, y1).
0 = (-3/2)(2) + b
Step 3: Solve for the y-intercept (b):
0 = -3 + b
b = 3
Step 4: Substitute the values of the slope (m) and y-intercept (b) into the equation:
y = -3/2x + 3
Therefore, the equation for the line that passes through the coordinates (2,0) and (0,3) is y = -3/2x + 3.
So, the correct answer is (1) y = -3/2x + 3.
To find the equation of a line that passes through two given points, you can use the slope-intercept form of a linear equation, which is y = mx + b.
Step 1: Determine the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the coordinates given are (2,0) and (0,3).
So, m = (3 - 0) / (0 - 2) = 3 / (-2) = -3/2.
Step 2: Substitute the slope value into the equation, replacing the 'm':
y = (-3/2)x + b
Step 3: To find the y-intercept (b), substitute the x and y values of one of the given points into the equation:
Let's use the point (2,0):
0 = (-3/2)(2) + b
0 = -3 + b
b = 3
Step 4: Replace the 'b' value in the equation:
y = (-3/2)x + 3
Therefore, the equation for the line passing through the points (2,0) and (0,3) is y = (-3/2)x + 3.
Comparing the options provided:
(1) y = -3/2x + 3 - This is the correct equation we derived.
(2) y = -3/2x - 3 - The constant term is incorrect.
(3) y = -2/3x + 2 - Both the slope and constant terms are incorrect.
(4) y = -2/3x - 2 - The slope is incorrect.
Thus, the correct equation is (1) y = -3/2x + 3.