We have the given slope value and the coordinate point that the graph passes through.
[tex]y = mx + b[/tex]
where m = slope and b = y-intercept. Substitute the value of slope in the equation.
[tex]y = - \frac{3}{4} x + b[/tex]
We have the given coordinate point as well. After we substitute the slope, we substitute the coordinate point value in the equation.
[tex]3 = - \frac{3}{4} (4) + b \\ [/tex]
Solve the equation for b-term
[tex]3 = - 3 + b \\ 3 + 3 = b \\ 6 = b[/tex]
The value of b is 6. We substitute the value of b in the equation.
[tex]y = - \frac{3}{4} x + 6[/tex]
We can also use the Point-Slope form to solve the question.
[tex]y - y_1 = m(x - x_1)[/tex]
Given the y1 and x1 = the coordinate point value.
Substitute the slope and coordinate point value in the point slope form.
[tex]y - 3 = - \frac{3}{4} (x - 4)[/tex]
Simplify/Convert into Slope-intercept
[tex]y = - \frac{3}{4} (x - 4) + 3 \\ y = - \frac{3}{4} x + \frac{12}{4} + 3 \\ y = - \frac{3}{4} x + 3 + 3 \\y = - \frac{3}{4} x + 6[/tex]
[tex] \large \boxed {y = - \frac{3}{4} x + 6}[/tex]
