So I need help with 2 questions. This is what is being asked. Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
1. (3, -2) x - y =0
2. (-4, 1) y + 2 = 0
Please Help and Thank You
parallel lines have the same slope
perpendicular lines have slopes which are negative reciprocals. That is, m1 * m2 = -1
The line x-y=0 has slope=1
so, the point-slope form of the line you want is
y+2 = 1(x-3)
to change that to slope-intercept form, you want y = mx+b, so it's just a matter of rearranging the data
y+2 = 1(x-3)
y = x-3 - 2
y = x-5
The perpendicular line has slope -1, so it is thus
y+2 = -1(x-3)
y = -x+3 - 2
y = -x+1
Do the other line the same way.
L00K 1T UP G1R|_ F431ND
To find the slope-intercept form of the equation of a line, we need to find the slope (m) and the y-intercept (b) of the line.
(a) For lines parallel to the given line, they will have the same slope. So, to find the equation of a line parallel to the given line, we need to first find the slope of the given line, and then use that slope with the given point in the point-slope form of the equation.
1. Given line: x - y = 0
To find the slope of the given line, we need to rewrite it in slope-intercept form (y = mx + b).
x - y = 0
y = x
Now we can see that the slope of the given line is 1. So, any line parallel to this will have the same slope.
Using the point (3, -2), we can substitute it into the point-slope form: y - y1 = m(x - x1)
y - (-2) = 1(x - 3)
y + 2 = x - 3
y = x - 5
Therefore, the equation of the line through the point (3, -2) parallel to the given line is y = x - 5.
(b) For lines perpendicular to the given line, the slopes will be negative reciprocals of each other. So, to find the equation of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line, and then use that slope with the given point in the point-slope form of the equation.
2. Given line: y + 2 = 0
To find the slope of the given line, we need to rewrite it in slope-intercept form (y = mx + b).
y + 2 = 0
y = -2
The slope of the given line is 0. Since the negative reciprocal of 0 is undefined, the equation of the line perpendicular to this does not exist. Therefore, there is no solution for the second question.
I hope this explanation helps! If you have any further questions, please let me know.