Math

QuestionFind the equation of the line passing through (1,2)(-1,-2) with a slope of 11.

Studdy Solution

STEP 1

Assumptions1. We are given a point (1,)(-1,-) through which the line passes. . We are given the slope of the line as 11.
3. We are to find the equation of the line in slope-intercept form, y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

STEP 2

We start by writing the general form of the equation of a line in slope-intercept form, which is y=mx+by = mx + b.
y=mx+by = mx + b

STEP 3

We substitute the given slope m=1m =1 into the equation.
y=1x+by =1x + b

STEP 4

We simplify the equation by removing the coefficient of 11 before xx.
y=x+by = x + b

STEP 5

To find the y-intercept bb, we substitute the given point (1,2)(-1,-2) into the equation. The x-coordinate of the point is 1-1 and the y-coordinate is 2-2.
2=1+b-2 = -1 + b

STEP 6

We solve for bb by adding 11 to both sides of the equation.
2+1=b-2 +1 = b

STEP 7

Calculate the value of bb.
b=1b = -1

STEP 8

Now that we have the y-intercept bb, we can write the final equation of the line by substituting bb back into the equation.
y=x1y = x -1The equation of the line that passes through the point (1,2)(-1,-2) with a slope of 11 is y=x1y = x -1.

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