Question

What is an equation of the line that passes through the points (2, -1) and (3,-4)?

Answer 1

Answer:

y=3x+5

Step-by-step explanation:

gradient =(y2-y1)÷(x2-x1)

(-4--3)÷(3-2)

=-3/1

y=mx+c

y+1/x-2=_3/1

y+1=-3x+6

y=3x+5

Answer 2

$\huge\underline\mathtt\colorbox{orange}{ y = -3 x + 5}$

Step-by-step explanation:

Find the equation of the line in slope-intercept form with the properties:

point: p_1 = (2, -1)

point: p_2 = (3, -4)

The slope of the line through points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1):

m = (-4 - (-1))/(3 - 2) = -3

Substitute the slope m = -3 and point (x_1, y_1) = (2, -1) into the point-slope equation y - y_1 = m (x - x_1):

y - (-1) = -3 (x - 2)

Subtract 1 from both sides:

y = -1 - 3 (-2 + x)

Distribute: -3 (x - 2) = 6 - 3 x:

Answer:

y = -3 x + 5