1.) Write the equation for the line in slope-intercept form:Slope: m=3; Y-intercept: B=7
*y - 3 = 7(x - 3)
*y = 3x + 7
*y = 7x - 3
2.)Write the equation for the line in slope-intercept form: Slope: m=4/3; Y-intercept: b=-2
*y = 4/3x - 2
*y + x = 2x + 1/2
*y = 1/2x - 2
3.)Which of the following lines is perpendicular to the line x + y = 3?
*3y + 3x = 1
*y = x + 1/2
*y = -x + 3
1) y= 3x + 7
2) y= 4/3x - 2
3) y= x + 1/2
To find a line that is perpendicular to the given line, x + y = 3, we need to find the negative reciprocal of the slope of the given line.
First, let's rewrite the given line in slope-intercept form (y = mx + b):
x + y = 3
y = -x + 3
The slope of this line is -1.
To find the negative reciprocal, we flip the fraction and change the sign:
The negative reciprocal of -1 is 1.
Now, let's look at the answer choices:
1) 3y + 3x = 1
2) y = x + 1/2
3) y = -x + 3
To determine which line is perpendicular, we can compare their slopes.
1) The equation 3y + 3x = 1 can be rewritten as y = -x + 1/3. The slope of this line is -1/3, which is not the negative reciprocal of -1. So, this line is not perpendicular.
2) The equation y = x + 1/2 has a slope of 1, which is the negative reciprocal of -1. Therefore, this line is perpendicular to x + y = 3.
3) The equation y = -x + 3 has a slope of -1, which is not the negative reciprocal of -1. So, this line is not perpendicular.
Therefore, the line y = x + 1/2 is the line that is perpendicular to x + y = 3.