A line has y-intercept (0, 3) and is perpendicular to the line 2x + y = 3. Find the x-intercept of the line.
To find the x-intercept of the line perpendicular to the line 2x + y = 3, we need to first find the slope of the given line.
We can rewrite the equation of the given line, 2x + y = 3, in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation, we get:
y = -2x + 3
From this equation, we can see that the slope of the given line is -2.
Since the line we are looking for is perpendicular to the given line, the slope of the perpendicular line will be the negative reciprocal of -2. The negative reciprocal of -2 is 1/2.
Now we have the slope (m) of the perpendicular line. We also know the y-intercept of the line is (0, 3).
Using the slope-intercept form of a line, y = mx + b, we can substitute the values of m and b to get the equation of the perpendicular line:
y = (1/2)x + 3
To find the x-intercept of this line, we set y to 0 and solve for x:
0 = (1/2)x + 3
Subtracting 3 from both sides:
-3 = (1/2)x
Multiplying both sides by 2 to eliminate the fraction:
-6 = x
Therefore, the x-intercept of the line perpendicular to the line 2x + y = 3 is -6.
since the given line has slope -2, we want slope 1/2.
So, y = x/2 + b
Since when x=0, y=3, b=3 and
y = x/2 + 3
So, when y=0, x=?
So would the answer be 6 or 3 then
Neither, it would be -6
taking Steve's equation of y= x/2 + 3 , and letting y = 0
0 = x/2 + 3
-3 = x/2
-6 = x