Answer:
Please check the explanation.
Step-by-step explanation:
Given the points
Finding the slope between (2, 17), (4, 7)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(2,\:17\right),\:\left(x_2,\:y_2\right)=\left(4,\:7\right)[/tex]
[tex]m=\frac{7-17}{4-2}[/tex]
[tex]m=-5[/tex]
We know the Point-Slope Form of the line equation is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Here:
substituting the values m = -5 and the point (2, 17) in the Point-Slope Form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - 17 = -5 (x-2)[/tex]
Thus, the answer Point-Slope Form is
[tex]y - 17 = -5 (x-2)[/tex]
It can be further simplified to write into the Slope-Intercept Form
[tex]y - 17 = -5 (x-2)[/tex]
y-17 = -5x+10
y = -5x+10+17
y = -5x+27
Thus, the answer in the Slope-Intercept Form (y=mx+b)
y = -5x+27 ∵Slope-Intercept Form → y=mx+b
