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Hi Brainly user! I'll answer your question.
First we're going to use the two points and the slope formula to find the slope of the line.
The slope formula is:
[tex]\sf m=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values:
[tex]\sf m=\cfrac{7-(-2)}{4-1}[/tex]
[tex]\sf m=\cfrac{7+2}{3}[/tex]
[tex]\sf m=\cfrac{9}{3}[/tex]
[tex]\sf m=3[/tex]
Now that we know the slope, we are going to use the first point and the point-slope formula to determine the equation.
The point-slope formula is:
Substitute the values:
[tex]\sf y-(-2)=3(x-1)[/tex]
[tex]\sf y+2=3(x-1)[/tex]
[tex]\sf y+2=3x-3[/tex]
[tex]\sf y=2x-3-2[/tex]
[tex]\sf y=2x-5[/tex]
Therefore, the line's equation is y = 2x - 5.