Question

What is the equation of the line with a slope of 3/4 that goes through the point (4, 1) in slope-intercept form?

Answer 1

`y=(3)/(4)x+-2`

Explanation:

We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is
`y -y_(1) =m(x -x_(1))` where we substitute a point (x,y) for
`(x_(1),y_(1))`.

We have m=3/4 and (4, 1). We input m and
`x_(1) =4\\y_(1)=1`.

`y-1=(3)/(4) (x-4)`

We now simplify the parenthesis and solve for y.

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

We convert -4 into a fraction with 1 as the denominator.

`y-1=(3)/(4)x+(3)/(4) ((-4)/(1) )\\y-1=(3)/(4)x+(-12)/(4)\\y-1=(3)/(4)x+-3`

We add 1 to both sides to isolate y,

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

This is slope intercept form. The line as slope 3/4 and y-intercept (0,2) or b=2.