Question

Find the equation of the line using the point-slope formula. Write the final equation using slope-intercept form. (1,2) with a slope of -3/4

So because I am horrible at Algebra I would kindly like to ask somebody to assist me if they are willing please and thank you.

Answer 1

`y-2=\displaystyle -(3)/(4)(x-1)`

OR

`y=\displaystyle -(3)/(4)x+(11)/(4)`

Explanation:

Hi there!

Point-slope form:
`y-y_1=m(x-x_1)` where m is the slope of the line and
`(x_1,y_1)` is a given point

Given that the slope is -3/4, we can plug it into
`y-y_1=m(x-x_1)` as m:

`y-y_1=\displaystyle -(3)/(4)(x-x_1)`

We can also plug in the given point (1,2):

`y-2=\displaystyle -(3)/(4)(x-1)`

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

To write the equation in slope-intercept form, isolate y:

`y-2=\displaystyle -(3)/(4)(x-1)\\\\y=\displaystyle -(3)/(4)(x-1)+2\\\\y=\displaystyle -(3)/(4)x+(3)/(4)+2\\\\y=\displaystyle -(3)/(4)x+(11)/(4)`

I hope this helps!