Question

Write an equation of the line in slope-intercept form, standard form with a positive leading coefficient and integer values, and in point-slope form that passes through the points (-2,8) and (7,-5.5).

Answer 1

To write the equation of the line that passes through the points (-2,8) and (7,-5.5), we can find the slope using the formula and then use it to write the equation in slope-intercept form, standard form, and point-slope form.

Step-by-step explanation:

To write an equation of the line that passes through the points (-2,8) and (7,-5.5), we first need to find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

Substituting the coordinates (-2,8) and (7,-5.5) into the formula, we have:

m = (-5.5 - 8) / (7 - (-2)) = -13.5 / 9 = -1.5

Now that we have the slope, we can write the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's substitute one of the given points, (-2,8), into the equation:

8 = -1.5 * (-2) + b

Solving for b, we get:

b = 8 - (-3) = 11

Therefore, the equation of the line in slope-intercept form is y = -1.5x + 11.

To find the equation of the line in standard form, we can rearrange the slope-intercept form equation:

1.5x + y = 11

Now, let's write the equation of the line in point-slope form using the coordinates (-2,8) and the slope -1.5:

y - 8 = -1.5(x - (-2))

Simplifying the equation, we get:

y - 8 = -1.5(x + 2)

y - 8 = -1.5x - 3

Therefore, the equation of the line in point-slope form is y - 8 = -1.5x - 3.