Answer :
Hello!
We know that:
• Slope ,= 3
,• The, line passes through the point, (7, 2)
Knowing it, let's answer your exercise:
What is the point-slope of the equation of the line?
First, we have to remember how to write the point-slope equation:
[tex]y-y_1=m\mleft(x-x_1\mright)[/tex]As we know the values, we just have to replace them:
[tex]y-2_{}=3(x-7_{})[/tex]What is the slope-intercept form of the equation of the line?
The slope-intercept form is:
[tex]y=mx+b[/tex]We have to calculate the y-intercept (b). So, let's do it by replacing the point and slope in the variables:
[tex]\begin{gathered} 2=3\cdot7+b \\ 2=21+b \\ 2-21=b \\ b=-19 \end{gathered}[/tex]So, the slope-intercept form is:
[tex]y=3x-19[/tex]