Answer:
[tex]y-2=-\frac{3}{4} (x-7)[/tex]
Step-by-step explanation:
We are given that a line passes through (7, 2) and (3, 5). We want to write the equation of this line in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
First, we need to find the slope.
We need to find the slope (m) of the line.
We can use the following formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.
Though we already have the values of the points, we can label the values of the points to avoid confusion and mistakes.
[tex]x_1=7\\y_1=2\\x_2=3\\y_2=5[/tex]
Now, substitute into the equation.
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{5-2}{3-7}[/tex]
[tex]m = -\frac{3}{4}[/tex]
Substitute [tex]-\frac{3}{4}[/tex] as m in [tex]y-y_1=m(x-x_1)[/tex].
We get:
[tex]y-y_1=-\frac{3}{4} (x-x_1)[/tex]
Now, substitute 7 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].
We get:
[tex]y-2=-\frac{3}{4} (x-7)[/tex]
