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Chapter 4: Q. 396 (page 537)

In the following exercises, find the equation of a line with a given slope and y-intercept. Write the equation in slope-intercept form.

Slope-34and y-intercept (0,-2).

Short Answer

Expert verified

The equation of the line with the given slope -34and y-intercept (0,-2)is y=-34x-2.

Step by step solution

01

Step 1. Given data      

We have to find the equation of the line.

For that we have,

Slope m=-34

y-intercept=(0,-2)

02

Step 2. Equation of the line  

We have the point-slope formula y鈭�y1=m(x鈭�x1)

Where mis the slope and (x1,y1)is a point through which the line passes.

Here,

m=-34(x1,y1)=(0,鈭�2)

Let us substitute these in the point-slope formula,

That is,

y鈭�(鈭�2)=-34(x鈭�0)y+2=-34(x鈭�0)

Now we have to rewrite this into slope-intercept form, that isy=mx+b

Therefore, substracting from both sides of the equation we get,

localid="1647360513878" y+2鈭�2=-34xy=-34x鈭�2

Hence y=-34x鈭�2is the equation of the line with slope -34and y-intercept (0,-2).

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