Answer :
Answer:
The equation of the line will be:
[tex]y=\frac{5}{3}x-1[/tex]
Step-by-step explanation:
Given the points
- (3, 4)
- (12, 9)
Finding the slope between (3, 4) and (12, 9)
[tex]\left(x_1,\:y_1\right)=\left(3,\:4\right),\:\left(x_2,\:y_2\right)=\left(12,\:19\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{19-4}{12-3}[/tex]
[tex]m=\frac{5}{3}[/tex]
The equation of the line can be obtained using the point-slope form of the equation of the line
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 5/9 and the point (3, 4)
[tex]y-4=\frac{5}{3}\left(x-3\right)[/tex]
[tex]y-4+4=\frac{5}{3}\left(x-3\right)+4[/tex]
[tex]y=\frac{5}{3}x-1[/tex]
Therefore, the equation of the line will be:
[tex]y=\frac{5}{3}x-1[/tex]