Answer:
[tex]y=-\frac{3}{4}x+7[/tex]
Step-by-step explanation:
The slope is already given as [tex]-\frac{3}{4}[/tex] so all we have to do is solve for y-intercept
First, write the equation in slope-intercept form
[tex]y=-\frac{3}{4}x+b[/tex]
Next, use the point to substitute the x and y value and solve for the y-intercept
[tex]y=-\frac{3}{4} x+b[/tex] where b = y-intercept
point: (8, 1)
[tex]1=-\frac{3}{4}(8)+b[/tex]
Then multiply 8 and -3/4
[tex]1=-6+b[/tex]
Finally, solve for the b (y-intercept)
b = [tex]1--6[/tex]
b = 7
so the y-intercept is 7
And the equation of the line that passes through the point (8, 1) and has a slope of -3/4 is [tex]y=-\frac{3}{4}x+7[/tex]
