Answer:
[tex]\boxed {\boxed {\sf 2. \ y= -2x+17}}[/tex]
Step-by-step explanation:
We are given a point and a slope, so we can use the point-slope formula.
[tex]y-y_1=m(x-x_1)[/tex]
where m is the slope and (x₁, y₁) is a point the line passes through.
For this problem, the slope is -2 and the point is (5,7). Therefore:
[tex]m= -2 \\x_1= 5\\y_1= 7[/tex]
Substitute the values into the formula.
[tex]y-7= -2(x-5)[/tex]
We want to solve for y, because the standard form of a line is y=mx+b (where m is the slope and b is the y-intercept).
Distribute the -2.
[tex]y-7= (-2*x ) + (-2*-5)[/tex]
[tex]y-7= -2x+10[/tex]
7 is being subtracted from y. The inverse of subtraction is addition, so add 7 to both sides.
[tex]y-7+7=-2x+10+7\\y= -2x+17[/tex]
The equation of the line is y= -2x+17
