Question

Write the equation of the line that passes through the points (4,1) and (-6,9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.​

Answer 1

STANDARD FORM:

y = mx + b, where m is slope and b is y-intercept.

ANSWER:

First we will find the slope and then y-intercept.

slope(m) = y2 - y1/x2 - x1

• 9 - 1/- 6 - 4
• - 8/10
• - 4/5.

Now, 1 = - 4/5 × 4 + b

1 = - 16/5 + b

b = 1 + 16/5

b = 5 + 16/5

b = 21/5.

So, equation becomes

• y = - 4/5x + 21/5.

Answer 2

Answer:

Find the slope:

• $m = \frac{y2-y1}{x2-x1} = \frac{9 - 1}{-6 - 4} = -\frac{8}{10} = -\frac{4}{5}$

Use point-slope form and one of the points:

• y - y₁ = m(x - x₁)
• $y - 1 = -\frac{4}{5}(x - 4)$