Answer:
Step-by-step explanation:
The equation for a line can be written in slope-intercept form:
[tex]y = mx + b[/tex]
Where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept.
Since we know "[tex]y[/tex] increases by [tex]4[/tex] when [tex]x[/tex] increases by [tex]1[/tex]", that tells us that the slope of the line is [tex]4[/tex].
[tex]y = 4x + b[/tex]
To figure out the y-intercept, [tex]b[/tex], we can plug in the coordinates given in the problem to the point that the line passes through, [tex](2, -1)[/tex]
[tex]1 = 4(2) + b[/tex]
[tex]1 = 8 + b[/tex]
[tex]b = -7[/tex]
Therefore, the equation of the line is [tex]y = 4x - 7[/tex]
