Line s has an equation of y = x − 8 .
Line t includes the point (1, 2) and is perpendicular to line s . What is the equation of line t ?

Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

The answer is y=-x+3

Step-by-step explanation:

The first step to do is to figure out what angle the perpendicular would be at:

Considering that line s has a slope of 1, then line t would have a slope of -1

Quick Check:

A perpendicular line is the inverse of the original line, giving it an angle of 90°  where they intersect. You'll find it by flipping the numerator and denominator of a fraction them making it negative.

The next step is to line it up with the point (1,2). The y-intercept does not change when you're making a line perpendicular.

So the equation so far is y = -x -8, note that's not the answer

The last step is to simply use logic, as if a line needs to intersect with a point on a graph, you can just backtrack.

Knowing that each x value that you move forward on the graph, the you go down 1 on the y axis, by using 3 as the y-intercept, you're on the right track.

By using (0,3) as the y-intercept, and moving right 1 and then down 1 (to match with line t's slope), you'll get to the point (1, 2)

The final answer as a result of this will be:

y=-x+3

y = - x + 3

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

c represents the y intercept

The equation of the given line s is

y = x - 8

Comparing with the slope intercept form, slope = 1

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of line t passing through (1, 2) is - 1

To determine the y intercept, we would substitute m = - 1, x = 1 and

y = 2 into y = mx + c. It becomes

2 = - 1 × 1 + c

2 = - 1 + c

c = 2 + 1 = 3

The equation becomes

y = - x + 3