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Chapter 2: Q. 29. (page 79)

Write an equation in slope-intercept form for the line that satisfies each set of conditions.

passes through -2,5 and 3,1

Short Answer

Expert verified

The equation of the required straight line in slope-intercept form is y=-45x+175.

Step by step solution

01

Step 1. State the concept

The slope intercept form of a straight-line equation is y=mx+c where m is the slope and c is the y-intercept.

The equation of a straight-line passing through the points h,kand a,bis given as y-kx-h=b-ka-h.

02

Step 2. List the given data

It is given that the line passes through -2,5 and 3,1.

Then, h,k=-2,5 and a,b=3,1.

03

Step 3. Write the equation

Put h,k=-2,5 and a,b=3,1 in y-kx-h=b-ka-h to get,

y-5x--2=1-53--2

y-5x+2=-43+2 (Simplify)

y-5x+2=-45 (Simplify)

y-5x+2x+2=-45x+2 (Multiply both sides by x+2)

y-5=-45x+2 (Simplify)

y-5=-45x-85 (Distributive property)

y-5+5=-45x-85+5 (Add 5 to both sides)

y=-45x+175 (Simplify)

So, the required equation of the straight line in slope-intercept form is y=-45x+175.

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