Answer:
[tex]y-2=\displaystyle -\frac{3}{4}(x-1)[/tex]
OR
[tex]y=\displaystyle -\frac{3}{4}x+\frac{11}{4}[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope of the line and [tex](x_1,y_1)[/tex] is a given point
Given that the slope is -3/4, we can plug it into [tex]y-y_1=m(x-x_1)[/tex] as m:
[tex]y-y_1=\displaystyle -\frac{3}{4}(x-x_1)[/tex]
We can also plug in the given point (1,2):
[tex]y-2=\displaystyle -\frac{3}{4}(x-1)[/tex]
Slope-intercept form: [tex]y=mx+b[/tex] 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:
[tex]y-2=\displaystyle -\frac{3}{4}(x-1)\\\\y=\displaystyle -\frac{3}{4}(x-1)+2\\\\y=\displaystyle -\frac{3}{4}x+\frac{3}{4}+2\\\\y=\displaystyle -\frac{3}{4}x+\frac{11}{4}[/tex]
I hope this helps!
