Question

Write the equation of the line in slope intercept form that passes through the points (-1,1) and (2,13)

Answer 1

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-1, 1) and (2, 13). Substitute:

$m=\dfrac{13-1}{2-(-1)}=\dfrac{12}{3}=4$

Therefore the equation of a line is

$y=4x+b$

Put the coordinates of the point (2, 13) to the equation of a line:

$13=4(2)+b$

$13=8+b$     subtract 8 from both sides

$5=b\to b=5$

Answer: y = 4x + 5