Question

writing an equation given two points on the line

write the equation of the line that passes through the points \\((7, -4)\\) and \\((-1, 3)\\), first in point-slope form, and then in slope-intercept form.

the slope of the line is \\(-7/8\\)
when the point \\((7, -4)\\) is used, the point-slope form of the line is
the slope-intercept form of the line is

Explanation:

Calculate the slope of the line

Using the Slope Formula knowledge point

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-4)}{-1 - 7} = \frac{7}{-8} = -\frac{7}{8} $$

Write the point-slope form

Using the Point-Slope Form knowledge point

$$
LATEXBLOCK0
$$

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Answer:

Write the equation of the line that passes through the points \((7, -4)\) and \((-1, 3)\), first in point-slope form, and then in slope-intercept form.

The slope of the line is <blank>\(-\frac{7}{8}\)</blank>.
When the point \((7, -4)\) is used, the point-slope form of the line is <blank>\(y + 4 = -\frac{7}{8}(x - 7)\)</blank>.
The slope-intercept form of the line is <blank>\(y = -\frac{7}{8}x + \frac{17}{8}\)</blank>.