Answer:
[tex]y=-\frac{1}{2}=-0.5[/tex]
Step-by-step explanation:
Given points :
(2,3) and (5,y)
Slope of line = [tex]-\frac{7}{6}[/tex]
To find the value of [tex]y[/tex].
We will apply the slope formula to find slope using the given points.
Slope [tex]m[/tex] of a line with points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plunging in the given points (2,3) and (5,y) in the formula.
[tex]m=\frac{y-3}{5-2}[/tex]
[tex]m=\frac{y-3}{3}[/tex]
We know the slope of line = [tex]-\frac{7}{6}[/tex]
So, we will equate and solve for [tex]y[/tex]
[tex]\frac{y-3}{3}=-\frac{7}{6}[/tex]
Multiplying both sides by 6 to remove fractions.
[tex]6\times \frac{y-3}{3}=6\times-\frac{7}{6}[/tex]
[tex]2(y-3)=-7[/tex]
Using distribution.
[tex]2y-6=-7[/tex]
adding 6 both sides.
[tex]2y-6+6=-7+6[/tex]
[tex]2y=-1[/tex]
Dividing both sides by 2.
[tex]\frac{2y}{2}=-\frac{1}{2}[/tex]
∴ [tex]y=-\frac{1}{2}=-0.5[/tex] (Answer)
