Question

Write the equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 and graph​

Answer 1

The equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 is: y=-x+3

Explanation:

Given equation of line is:

`y = x+2`

Comparing it with the general form of equation of line in slope-intercept form

`y = mx+b`

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

`m.m_1 = -1\\1.m_1 = -1\\m_1 = -1`

The equation of new line perpendicular to given line will be:

`y = m_1x+b`

Putting the value of m1

`y = -x+b`

To find the value of b, the given point will be put into the equation

So,

`-1 = -(4)+b\\-1 = -4+b\\-1+4 = b\\b = 3`

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:

`y = -x+3`

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