Question

Write an equation for the line passing through the given pair of points. Give the final answer in (a) slope-intercept form and (b) standard form.

(2,9) and (3,10)
(a) The equation of the line in slope-intercept form is y=3x +3
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Answer 1

To find the equation of the line passing through the points (2,9) and (3,10), you can use the point-slope form of a linear equation:

First, calculate the slope (m) using the given points:

m = (y2 - y1) / (x2 - x1) = (10 - 9) / (3 - 2) = 1 / 1 = 1

Next, use one of the points and the calculated slope in the point-slope form:

y - y1 = m(x - x1)

Using the point (2,9):

y - 9 = 1(x - 2)

Simplify:

y - 9 = x - 2

Now, solve for y to get the equation in slope-intercept form (y = mx + b):

y = x - 2 + 9

y = x + 7

So, the equation of the line in slope-intercept form is:

y = x + 7

(b) To write the equation in standard form, you can move the x and y terms to the left side of the equation and bring the constant to the right side:

x - y = -7

This is the equation of the line in standard form.