Answer:
The equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 is: y=-x+3
Step-by-step explanation:
Given equation of line is:
[tex]y = x+2[/tex]
Comparing it with the general form of equation of line in slope-intercept form
[tex]y = mx+b[/tex]
The slope of given line is 1 as the co-efficient of x in the equation is 1.
When two lines are perpendicular, the product of their slopes is -1
Let m1 be the slope of new line
Then
[tex]m.m_1 = -1\\1.m_1 = -1\\m_1 = -1[/tex]
The equation of new line perpendicular to given line will be:
[tex]y = m_1x+b[/tex]
Putting the value of m1
[tex]y = -x+b[/tex]
To find the value of b, the given point will be put into the equation
So,
[tex]-1 = -(4)+b\\-1 = -4+b\\-1+4 = b\\b = 3[/tex]
The final equation of line is: y = -x+3
Hence,
The equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 is:
[tex]y = -x+3[/tex]
Graph:(Attached)
The graph is made using the online graphing tool "Desmos". The red line in the graph represents the line y = x+2 and the blue line represents the line (y=-x+3) perpendicular to given line
