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

Answer:

$y=\frac{3}{4}x+-2$

Step-by-step 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 $x_{1} =4\\y_{1}=1$.

$y-1=\frac{3}{4} (x-4)$

We now simplify the parenthesis and solve for y.

$y-1=\frac{3}{4} (x-4)\\y-1=\frac{3}{4}x+\frac{3}{4} (-4)$

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

$y-1=\frac{3}{4}x+\frac{3}{4} (\frac{-4}{1} )\\y-1=\frac{3}{4}x+\frac{-12}{4}\\y-1=\frac{3}{4}x+-3$

We add 1 to both sides to isolate y,

$y-1+1=\frac{3}{4}x+-3+1\\y=\frac{3}{4}x+-2$

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